Exponents And Powers - Class 8 Maths - Extra Questions

Evaluate : $$\left (\dfrac 8{125}  \right )^{-\tfrac13}$$



$$\left ( \dfrac{-1}{27} \right )^{-2/3}$$



Identify the greater number, wherever possible, in the following.
$$2^{10}$$ or $$10^{2}$$.



Express the number appearing in the following statement in standard form.
The earth has $$1,535,000,000$$ cubic $$km$$ of seawater.



Express the number appearing in the following statement in standard form.
Diameter of the Earth is $$1,27,56,000$$ meters.



Express the the mean distance between Earth and moon is $$384,000,000\ m$$ in standard from.



Express the number appearing in the following statement in standard from.
The univers is estimated to be $$12,000,000,000$$ years old.



Express the number appearing in the following statement in standard from:
The distance between Sun and Saturn is $$1,433,000,000,000\ m\ .$$



Write the given product in exponential form.
$$7\times a\times a\times a..... 8$$ times $$\times b\times b\times b\times … 5$$ times.



Write the given expression in the product form.
$$30x^4y^4z^5$$



Write the given product in exponential form.
$$4\times a\times a\times ….. 5\text{ times }\times b\times b\times ….. 12\text{ times }\times c\times c..... 15\text{ times }$$.



Express the numbers appearing in the following statements in the standard form:
The universe is estimated to be about 12,000,000,000 years old.



Express the numbers appearing in the following statements in the standard form:
Diameter of the Earth is 1,27,56,000 metres.



Evaluate $$64^{\tfrac{-1}{2}}$$.



Identify the greater number, wherever possible, in the following?
$$100^2$$ or $$2^{100}$$.



Identify the greater number in the following.
$$2^8$$ or $$8^2$$.



Write the following number in standard form:
$$\dfrac{1}{1000000}$$.



Evaluate
$$\left(\dfrac 3 5\right)^{-2}$$



Express the number appearing in the following statement in standard from.
$$60,230,000,000,000,000,000,000$$ molecules are present in a drop of water weighing $$1.8\ gm$$.



Which is greater?
$$\left (\dfrac{1}{2}  \right )^{\frac{1}{2}}$$ or $$\left (\dfrac{2}{3}  \right )^{\frac{1}
{3}}$$ 



Prove that:
$$(\sqrt{3 \times 5^{-3}} \div \sqrt [ 3 ]{ 3^{ -1} } \sqrt{5}) \times \sqrt [ 6 ]{ 3 \times 5^6 } = \dfrac{3}{5}$$



Express $$16^{-2}$$ as a power with base $$4$$



Which is greater $$7^{92}$$ or $$8^{91}$$?



Which is larger: $${ \left( 100 \right)  }^{ 4 }$$ or $$ { \left( 125 \right)  }^{ 3 }$$?



Simplify and give reasons
$$\left(\dfrac{3}{4}\right)^{-3}$$



Express the following in standard from:
i) $$76854000\times 10^{8}$$
ii) $$0.000089\times 10^{6}$$



Simplify $$\displaystyle \frac { \left( 5 ^ { - 3 } \right) ^ { 2 } \times 3 ^ { 4 } } { \left( 3 ^ { - 2 } \right) ^ { - 3 } \times \left( 5 ^ { 3 } \right) ^ { - 2 } }$$



Compare the following numbers:
$$2.7\times{10}^{12};1.5\times{10}^{8}$$



Simplify and write the answer in exponential form
$${ \left( -4 \right)  }^{ -3 }\times { \left( 5 \right)  }^{ 3 }\times { \left( -5 \right)  }^{ -3 }$$



Evaluate $$\left\{\left(\dfrac{4}{3}\right)^{-1}-\left(\dfrac{1}{4}\right)^{-1}\right\}^{-1}$$



Express $$512$$ in power notation.



Prove that:
$${ \left\{ { \left( \dfrac { 1 }{ 3 }  \right)  }^{ -1 }-{ \left( \dfrac { 1 }{ 4 }  \right)  }^{ -1 } \right\}  }^{ -1 } = -1$$



Say true or false and justify your answer:
$${2}^{3}> {5}^{2}$$



Evaluate:
$$\left[\left(-\dfrac{2}{3}\right)^{-2}\right]^3\times \left(\dfrac{1}{3}\right)^{-4}\times 3^{-1}\times \dfrac{1}{6}$$



Find:
$$125^{\frac{-1}{3}}$$



Evaluate
$$(-3)^{-3}$$



Evaluate:
(i) $${\left (\dfrac{1}{3}\right )^{-1} - \left (\dfrac{1}{4}\right )^{-1}} $$
(ii) $$\left (\dfrac{5}{8}\right )^{-7}\times \left (\dfrac{8}{5}\right )^{-4} $$



Which is greater $$(150)^{300}$$ or $$(20000)^{100}\times (100)^{100}$$?



Evaluate:
(i) $$3^{-2}$$
(
ii) $$(-4)^{-2}$$
(iii) 
$$\left (\dfrac{1}{2}\right)^{-5}$$



Show that $$(1.1)^{10000} > 1000$$



Find $$x$$ in the expression $$(18)^{3.5}\div (27)^{3.5}\times 6^{3.5}=2^{x}$$



Mass of the earth is $$5.97\times {10}^{24}\ kg$$ and mass of the moon is $$7.35\times {10}^{22}\ kg$$. What is the difference of their masses?



Compare $$7 \times 10^{-6}$$ and $$129 \times 10^{-7}.$$



Which one is greater between $$31^{14}$$ and $$17^{18}$$?



Express the following in the decimal form:
$$4.67\times {10}^{4}$$



Simplify: $$\left(\dfrac{81}{16}\right)^{-3/4} \times \left(\dfrac{25}{9}\right)^{-3/2} \times \left(\dfrac{2}{5}\right)^{-3}$$



Find the value of $$x$$ for which$${ \left\{ { \left( \dfrac { -2 }{ 7 }  \right)  }^{ 2 } \right\}  }^{ x }\times { \left( \dfrac { -7 }{ 2 }  \right)  }^{ -1 }=\dfrac { -8 }{ 343 }$$.



If $$9^{x} \times 3^{2}\times \left(3^{\left(\tfrac{-x}{2}\right)}\right)^{-2}=\dfrac{1}{27}$$, then find the value of $$x$$.



If $$\left(\dfrac{5}{3}\right)^{-15} \times \left(\dfrac{5}{3}\right)^{11} =\left(\dfrac{5}{3}\right)^{8x}$$, then $$x$$ =?



If the standard form of $$12,000,000,000$$ is $$1.2\times 10^{m}$$ then find the value of $$m$$.



If $${ \left( 64 \right)  }^{ x }=\cfrac { 1 }{ { \left( 256 \right)  }^{ y } } =2\sqrt { 2 } $$; then show that $$3x+4y=0$$.



If $$2^{x-1}+2^{x+1}=1280$$, then find the value of $$x$$.



Identify the greater number, wherever possible, in the following?
$$5^3$$ or $$3^5$$.



If $$x^{1/p} = y^{1/q} = z^{1/r}$$ and $$xyz = 1, $$ then the value of $$p+q+r = ? $$



Identify the greater number between the following:
$$4^3$$ or $$3^4$$



Which is greater among the following?
$$\sqrt{2}, \sqrt[3]{4}$$ and $$ \sqrt[4]{3}$$



$$\begin{array}{l} If\, \, { e^{ \left( { { { \sin   }^{ 2 } }x+{ { \sin   }^{ 2 } }x+{ { \sin   }^{ 6 } }x......\infty  } \right) \log { e^{ 2 } }  } }\, and\, { y^{ 2 } }-5y+4=0\, satisfy\, the\, equation\, then\, find\, the\,  \\ value\, of\, \frac { { \sin  x } }{ { \cos  x-\sin  x } }  \end{array}$$



Write the base and the exponent of $$(7x)^{2}$$



Change the given number into it's standard form
$$128000000$$



$$(\sqrt [ 5 ]{ 8 } )^{\dfrac{5}{2}}\times (16)^{\dfrac{-3}{2}}$$



Express the following as a product of prime factors in exponential form : 
$$729\times 64$$



Identify the greater number in each of the following numbers:
$${2}^{8}$$ or $${8}^{2}$$



Identify the greater number among the two numbers:
$${2}^{10}$$ or $${10}^{2}$$



Identify the greater number in the following numbers:
$${100}^{2}$$ or $${2}^{100}$$



Express the number appearing in the following statements in standard form:
$$602,300,000,000,000,000,000,000$$ molecules are contained in a drop of water weighing $$1.8gm$$.



Write $$629000$$ in standard form.



Express the number appearing in the following statement in standard form:
The Earth has $$1,353,000,000$$ cubic km of seawater.



Identify the greater number, wherever possible, in each of the following:
$${5}^{3}$$ and $${3}^{5}$$



On solving the equation $$ 7^{2x+3} = 1 $$, we get $$x=\dfrac{-3}{b}$$ then find the value of $$b$$.



Standard from of $$6020000000000000$$ is $$6.02\times 10^{16}$$.
Enter 1 if it is True or 0 if it is False



Express the following numbers in standard from:
$$4 \div 100000$$



Write the given expression in the product form.
$$43p^{10}q^5r^{15}$$



Write the given product in exponential form.
$$8\times b\times b\times b\times a\times a\times a\times a$$.



Write the expression $$5xy\times 3x^2y\times 7y^2$$ in exponential form.



Write the given expression in the product form.
$$a^2b^5$$.



Write the given expression in the product form.
$$17p^{12}q^{20}$$.



Express the following number in standard form:
$$0.00000000000942$$



Express the following Number in the standard form:
$$ 846 \times 10^7 $$



find the product of
$$a^3\times 3ab^2\times 2a^2b^2$$.



Express the number $$5,00,00,000$$ in the standard from.



Write the given statement in the product form.
$$x^3y^4$$.



Write the following number in the usual form: 
$$ 4.83 \times 10^7 $$



Express the following Numbers in the standard from: $$ 723 \times 10^9 $$



The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two-third of its breadth. Find its area, if its breadth is x cm.



Simplify $$\left(\dfrac{81}{49}\right)^{-\tfrac{3}{2}}$$.



Write the following in ascending order of magnitude.
$$\sqrt[6]{6}, \sqrt[3]{7}, \sqrt[4]{8}$$.



Evaluate $$8^{\tfrac{-1}{3}}$$.



If $$a=2, b=3$$ find the value of $$(a^b+b^a)^{-1}$$.



Simplify $$\left(\dfrac{7776}{243}\right)^{-\dfrac{3}{5}}$$.



Evaluate:
$$\left(\dfrac{1}{2}\right)^{-5}$$



Evaluate:
$$4^{-3}$$



Evaluate:
$$\left(\dfrac{4}{3}\right)^{-3}$$



Simplify $$\left(\dfrac{32}{243}\right)^{-\tfrac{4}{5}}$$.



If $$a=2, b=3$$ find the value of $$(a^a+b^b)^{-1}$$.



Evaluate:
$$\left\{\left(\dfrac{3}{2}\right)^{-2}\right\}^{2}$$



Evaluate $$\left\{\left(\dfrac{1}{3}\right)^{-3}-\left(\dfrac{1}{2}\right)^{-3}\right\}\div \left(\dfrac{1}{4}\right)^{-3}$$



Evaluate : $$\left (1 \dfrac{61} {64}\right )^{-\tfrac{2} {3}}$$



Evaluate:
$$\left(\dfrac{2}{3}\right)^{-3}\times \left(\dfrac{2}{3}\right)^{-2}$$



Evaluate:
$$\left\{\left(\dfrac{-2}{3}\right)^{2}\right\}^{-2}$$



Evaluate:
$$\left(\dfrac{-2}{3}\right)^{-5}$$



Evaluate:
$$\left(\dfrac{-2}{3}\right)^{-3}\times \left(\dfrac{-2}{3}\right)^{-2}$$



Evaluate:
$$\left[\left\{\left(\dfrac{-1}{3}\right)^{2}\right\}^{-2}\right]^{-1}$$



Evaluate $$[\{(5^{-1})\times (3^{-1})\}^{-1}\div 6^{-1}]$$



Find the value of:
$$\left(\dfrac{1}{2}\right)^{-1}+\left(\dfrac{1}{3}\right)^{-2}+\left(\dfrac{1}{4}\right)^{-2}$$



Solve the following:
$$100^{-10}$$



Simplify :
$$\left( \dfrac{1}{4}\right)^{-2}+\left( \dfrac 12\right)^{-2}+\left( \dfrac 13\right)^{-2}$$



Simplify :
$$\left[ \left( \dfrac{-2}{3}\right)^{-2}\right]^{3}\times \left( \dfrac{1}{3}\right)^{-4}\times 3^{-1}\times \dfrac 16$$



Simplify :
$$\dfrac{49\times z^{-3}}{7^{-3}\times 10\times z^{-5}}( z\neq 0)$$



Express as a power of a rational number with negative exponent.
$$\left[ \left( \dfrac{-3}{2}\right)^{-2}\right]^{-3}$$



Find the value of $$[4^{-1}+3^{-1}+6^{-2}]^{-1}$$



If $$36=6 \times 6=6^2$$, then $$\dfrac{1}{36}$$ expressed as a power with base $$6$$ is ______.



The value of $$[3^{-1} \times \  4^{-1}]^2$$ is _______.



If $$\dfrac{5^m \times 5^3 \times 5^{-2}}{5^{-5}}=5^{12}$$. Find $$m$$.



Evaluate
$$(2/7)^{-4}$$



Consider a quantity of a radioactive substance. The fraction of this quantity that remains after $$t$$ half - lives can be found by using the expression $$3^{-t}$$.
What fraction of substance remains after $$7$$ half-lives?



In a shrinking machine, a piece of stick is compressed to reduce its length. If $$9\ cm$$ long sandwich is put into the shrinking machine below, how many $$cm$$ long will it be when it emerges?
1793339_eb4f53aba018449798bf5ae8032549b9.png



What happens when $$1\ cm$$ worms are sent through these hook-ups?
1793341_5f8d91854bfb42e799cbcaa84af7f12b.png



Find the value of
$$\dfrac{6^n}{6^{-2}}=6^3$$



Simplify
$$[(2)^{-1}+(4)^{-1}+(3)^{-1}]^{-1}$$



Evaluate:
$$(0.25)^{-1}$$.



Evaluate:
$$5^{-4} \times (125)^{\dfrac {5}{3}}- (25)^{-\dfrac 12}$$



Simplify:
$$(a+b)^{-1}, (a^{-1}+b^{-1})$$



Evaluate : $$\left (0.027  \right )^{-1/3}$$



$$(m+n)^{-1}(m^{-1}+n^{-1}) =(mn)^{-1}$$



Evaluate: $$\left ( \dfrac{81}{16} \right )^{-3/4}$$



$$\left (1\frac{61} {64}  \right )^{-\frac{2} {3}}$$



Prove that :
$$\dfrac{a^{-1}}{a^{-1}+b^{-1}}+\dfrac{a^{-1}}{a^{-1}-b^{-1}}=\dfrac{2b^2}{b^2-a^2}$$



Simplify each of the following and express with positive index:
$$[1-(1-(1-n)^{-1})^{-1}]^{-1}$$



$${ \left( \frac { 1 }{ 2 }  \right)  }^{ -2 }+{ \left( \frac { 1 }{ 3 }  \right)  }^{ -2 }+{ \left( \frac { 1 }{ 4 }  \right)  }^{ -2 }=?$$



Express the number appearing in the following statement in standard from.
Diameter of the sun is $$1,400,000,000 \text{ m}$$



By what a number should $$\left (\dfrac {5}{3}\right)^{-2}$$ be multiplied so that the product may be equal to $$\left (\dfrac {7}{3}\right)^{-1}$$?  



By what a number should $$\left (\dfrac {1}{2}\right)^{-1}$$ be multiplied so that the product may be equal to $$\left (\dfrac {-4}{7}\right)^{-1}$$?  



Express the number appearing in the following statement in standard from.
Mass of Uranus is $$86,800,000,000,000,000,000,000,000\ kg$$



The value of $$5\sqrt[4]{\sqrt[3]{5}}-\sqrt[3]{\sqrt[4]{5}}$$ is?



Class 8 Maths Extra Questions