Easy Algebra Step-by-Step

Rules for Exponents 75

Solution

a. xx^23 x

Step 1. Check for exponential expressions that have the same base.

xx^23

x^2 and x^3 have the same base, namely, x.

Step 2. Simplify xx^23. Keep the base x and add

the exponents 2 and 3.

xx^23 =xxx^235

b. xy^25 y

Step 1. Check for exponential expressions that have the same base.

x^2 y^5

x^2 and y^5 do not have the same base, so the

product cannot be simplifi ed.

c. xx^27 x yy^35 y

Step 1. Check for exponential expressions that have the same base.

xxyy

2 7 35

x

(^2) and x (^7) have the same base, namely, x, and y (^3) and y (^5) have the
same base, namely, y.
Step 2. Simplify xx^27 and yy^35. For each, keep the base and add the
exponents.
xx^27 yy^35 ==xyxy^277353 xy^98

Quotient Rule

Quotient Rule for Exponential Expressions with the Same Base

x

x

m

n

=≠xxmnmn, 0

This rule tells you that when you divide expo-

nential expressions that have the same base, you

subtract the denominator exponent from the

numerator exponent and keep the same base.

P

xx^23 x ≠=x^2323 x^6. When multiplying,

add the exponents of the same base,

don’t multiply them.

xy^25 y ≠(xy)^7. This is a common

error that you should avoid.

If the bases are not the same, don’t

use the quotient rule for exponential

expressions with the same base.