# Exponents And Powers For Class 8

The mass of Earth is 5970000000000000000000000 kg. It is really a challenging task to remember this number and even, it will be more painful in counting the number of zeros in the number.

With the help of exponent it is much easier to remember as well as representing the number in an easy manner. Any number to the power (also called exponent) can be represented in an easy way.

Various numbers can be easily expressed in the exponential form for easy of representation.

$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{7}$

Here the base value is 2 and the exponent is 7.

$7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7……..(m \; times) = 2^{m}$

Here the base value is 7 and exponent value is m, i.e. the multiplication of 7 takes m times, where m can take integral values.

Negative Power-

The negative power is similar to the normal exponent form, the only difference is that the repeated multiplication of the base takes place in the denominator.

$5^{-7} = \frac{1}{5^{7}}$

Laws of Exponents-

(i) $\frac{a^{m}}{a^{n}} = a^{m-n}$

(ii) $(a^{m})^{n} = a^{mn}$

(iii) $(a^{m}) \times (b^{m}) = (ab)^{m}$

(iv) $\frac{a^{m}}{b^{m}} = \left ( \frac{a}{b} \right )^{m}$

(v) $a^{0} = 1$

#### Practise This Question

Simplify:((15)3(13)4(14)3)