PROPERTIES OF EXPONENTS
In this section, we will learn the properties of exponents. We have listed the properties of exponents.
xm ⋅ xn = x(m + n) | If two or more terms are multiplying with the same base, we may write only one base and add the powers. |
xm / xn = x(m – n) | If two terms are dividing with the same base, we may write only one base and subtract the powers. |
(xm)n = xmn | If we have power raised to another power, then we should multiply both the powers |
x-m = 1/xm (or) (a/b)-m = (b/a)m | If we have negative exponent, then we can write the reciprocal form of the given number to make the negative exponent as positive. |
x0 = 1 | The value of anything to the power will be 1 |
Example problems on properties of exponents
Example 1 :
Simplify
2m2 ⋅ 3m3
Solution :
2m2 ⋅ 3m3 = 6m(2 + 3)
2m2 ⋅ 3m3 = 6m5
Example 2 :
Simplify

Solution :
(2x3/y3) ⋅ (x4/ y2) = 2x(3 + 4) / y(3 + 2)
= 2x7 / y5
Example 3 :
Simplify

Solution :
= 4g-4 b4 ⋅ 2gb-5
= 8g(-4 + 1) b(4 – 5)
= 8g-3 b– 1
= 8/g3b
Example 4 :
Simplify

Solution :
For all the terms, we have same base. So, we can write only one base and add the powers.
= (6/7)(4 + 2 + 3)
= (6/7)9