# Exponents and Powers - Class 8 - Mathematics

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## Examples - Exponents and Powers | NCERT | Mathematics | Class 8

Find the value of

(i) $2^{-3}$

(ii) $\frac{1}{3^{-2}}$

The values are as follows:

(i) $2^{-3} = \frac{1}{8} = 0.125$

(ii) $\frac{1}{3^{-2}} = 9$

Simplify

(i) $(-4)^{5} \times(-4)^{-10}$

(ii) $2^{5} \div 2^{-6}$

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Sign up nowExpress $4^{-3}$ as a power with the base 2.

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Sign up nowSimplify and write the answer in the exponential form.

(i) $\left(2^{5} \div 2^{8}\right)^{5} \times 2^{-5}$

(ii) $(-4)^{-3} \times(5)^{-3} \times(-5)^{-3}$

(iii) $\frac{1}{8} \times(3)^{-3}$

(iv) $(-3)^{4} \times\left(\frac{5}{3}\right)^{4}$

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Sign up nowFind $m$ so that $(-3)^{m+1} \times(-3)^{5}=(-3)^{7}$

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Find the value of $\left(\frac{2}{3}\right)^{-2}$.

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Simplify (i) $\left\{\left(\frac{1}{3}\right)^{-2}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-2}$

(ii) $\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-5}$

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Express the following numbers in standard form.

(i) 0.000035

(ii) 4050000

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Express the following numbers in usual form.

(i) $3.52 \times 10^{5}$

(ii) $7.54 \times 10^{-4}$

(iii) $3 \times 10^{-5}$

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## Exercise 10.1 - Exponents and Powers | NCERT | Mathematics | Class 8

Evaluate.

(i) $3^{-2}$

(ii) $(-4)^{-2}$

(iii) $\left(\frac{1}{2}\right)^{-5}$

The evaluations are as follows:

(i) $3^{-2}$ is equal to $$\frac{1}{9}$$

(ii) $(-4)^{-2}$ is equal to $$\frac{1}{16}$$

(iii) $\left(\frac{1}{2}\right)^{-5}$ is equal to $$32$$

Simplify and express the result in power notation with positive exponent.

(i) $(-4)^{5} \div(-4)^{8}$

(ii) $\left(\frac{1}{2^{3}}\right)^{2}$

(iii) $(-3)^{4} \times\left(\frac{5}{3}\right)^{4}$

(iv) $\left(3^{-7} \div 3^{-10}\right) \times 3^{-5}$

(v) $2^{-3} \times(-7)^{-3}$

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Find the value of

(i) $\left(3^{\circ}+4^{-1}\right) \times 2^{2}$

(ii) $\left(2^{-1} \times 4^{-1}\right) \div 2^{-2}$

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

(iv) $\left(3^{-1}+4^{-1}+5^{-1}\right)^{0}$$\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}$

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Evaluate (i) $\frac{8^{-1} \times 5^{3}}{2^{-4}}$

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Find the value of $m$ for which $5^{m} \div 5^{-3}=5^{5}$.

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

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Simplify.

(i) $\frac{25 \times t^{-4}}{5^{-3} \times 10 \times t^{-8}}(t \neq 0)$

(ii) (ii) $\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}$

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## Exercise 10.2 - Exponents and Powers | NCERT | Mathematics | Class 8

Express the following numbers in standard form.

(i) 0.0000000000085

(ii) 0.00000000000942

(iii) 6020000000000000

(iv) 0.00000000837

(v) 31860000000

The numbers expressed in standard form are as follows:

(i) $0.0000000000085$ in standard form is $8.5*10^{-12}$.

(ii) $0.00000000000942$ in standard form is $9.42*10^{-12}$.

(iii) $6020000000000000$ in standard form is $6.02*10^{15}$.

(iv) $0.00000000837$ in standard form is $8.37*10^{-9}$.

(v) $31860000000$ in standard form is $3.186*10^{10}$.

Express the following numbers in usual form.

(i) $3.02 \times 10^{-6}$

(ii) $4.5 \times 10^{4}$

(iii) $3 \times 10^{-8}$

(iv) $1.0001 \times 10^{9}$

(v) $5.8 \times 10^{12}$

(vi) $3.61492 \times 10^{6}$

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Express the number appearing in the following statements in standard form.

(i) 1 micron is equal to $\frac{1}{1000000} \mathrm{~m}$.

(ii) Charge of an electron is $0.000,000,000,000,000,000,16$ coulomb.

(iii) Size of a bacteria is $0.0000005 \mathrm{~m}$

(iv) Size of a plant cell is $0.00001275 \mathrm{~m}$

(v) Thickness of a thick paper is $0.07 \mathrm{~mm}$

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In a stack there are 5 books each of thickness $20 \mathrm{~mm}$ and 5 paper sheets each of thickness $0.016 \mathrm{~mm}$. What is the total thickness of the stack?