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 :
2m2 ⋅ 3m3
2m2 ⋅ 3m3 = 6m(2 + 3)
2m2 ⋅ 3m3 = 6m5
Example 2 :
(2x3/y3) ⋅ (x4/ y2) = 2x(3 + 4) / y(3 + 2)
= 2x7 / y5
Example 3 :
= 4g-4 b4 ⋅ 2gb-5
= 8g(-4 + 1) b(4 – 5)
= 8g-3 b– 1
Example 4 :
For all the terms, we have same base. So, we can write only one base and add the powers.
= (6/7)(4 + 2 + 3)