# Exponents And Powers Class 8

Exponents and Powers class 8 – For any non-zero integer p, $p^{-k}=\frac{1}{p^{k}}$, where m is a positive integer. Also, $p^{k}\times p^{m}=p^{k+m}$. Lets evaluate the value of $2^{-2}\;\;and\;\;\frac{1}{4^{-3}}$. Here, $2^{-2}=\frac{1}{2^{2}}=\frac{1}{4}=0.25$. Similarly, $\frac{1}{4^{-3}}= 4^{3}=64$

Example 1: Express 79,00,000,000 in standard form.

Solution: 79,00,000,00 = $7.9\times 10^{8}$

Numbers with negative exponents obey the following laws of exponents.

1. $\frac{a^{m}}{b^{m}}=\left ( \frac{a}{b} \right )^{m}$
2. $a^{0}=1$
3. $a^{m}\times b^{m}=\left ( ab \right )^{m}$
4. $\left ( a^{m} \right )^{n}=a^{mn}$

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

$\left ( \frac{8}{5} \right )^{7}\times \left ( \frac{5}{8} \right )^{5}=\frac{8^{2}}{5^{5}}=\frac{64}{25}$

### Exponents and Powers class 8 Examples

#### Practise This Question

What must be subtracted from x33x2+5x1 to get 2x3+x24x+2 ?