Question

Evaluate

a to the power x-b to the power
power x divide x​

Answer 1

Rule or special case Formula Example

Product xaxb=xa+b 2223=25=32

Quotient xaxb=xa−b 2322=21=2

Power of power (xa)b=xab (23)2=26=64

Power of a product (xy)a=xaya 36=62=(2⋅3)2=22⋅32=4⋅9=36

Power of one x1=x 21=2

Power of zero x0=1 20=1

Power of negative one x−1=1x 2−1=12

Change sign of exponents x−a=1xa 2−3=123=18

Fractional exponents xm/n=xm−−−√n=(x√n)m 43/2=(4√)3=23=8

The rules

Product of exponentials with same base

If we take the product of two exponentials with the same base, we simply add the exponents:

xaxb=xa+b.(1)

To see this rule, we just expand out what the exponents mean. Let's start out with a couple simple examples.

3432=(3×3×3×3)×(3×3)=3×3×3×3×3×3=36

y2y3=(y×y)×(y×y×y)=y×y×y×y×y=y5