Easy Algebra Step-by-Step

Rules for Exponents 77

c. xy

xy

(^75) y
(^23) y
Step 1. Check for exponential expressions that have the same base.
xy
xy
75
2 3
x
(^7) and x (^2) have the same base, namely, x, and y (^5) and y (^3) have the
same base, namely, y.
Step 2. Simplify
x
x
7
2 and
y
y
5
3. For each, keep the base and subtract the
exponents.
xy
xy
xy xy
75
2 3
==xy^72253552
d. x
x
3
10
Step 1. Check for exponential expressions that have the same base.
x
x
3
10
x^3 and x^10 have the same base, namely, x.
Step 2. Simplify
x
x
3
10. Keep the base x and subtract the exponents 3 and 10.
x
x
xx
3
10
=x^311070
Step 3. Express x−^7 as an equivalent exponential expression with a positive
exponent.
x
x
− (^7) =
7

1

Rules for Powers

Rule for a Power to a Power

()mp))) xmp

This rule tells you that when you raise an exponential expression to a

power, keep the base and multiply exponents.

P

When you simplify expressions,

make sure your fi nal answer does

not contain negative exponents.