Easy Algebra Step-by-Step

80 Easy Algebra Step-by-Step

Rules for Exponents

1. Product Rule for Exponential Expressions with the Same Base
   xxmnx =xmn+


2. Quotient Rule for Exponential Expressions with the Same Base
   x
   x

m

n

=≠xxmnmn, 0

3. Rule for a Power to a Power

x

p mp

()xm

4. Rule for the Power of a Product
   ()xyp=xyppy


5. Rule for the Power of a Quotient
   x
   y

x

y

y

p p

p

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

=≠,y 0

Notice there is no rule for the power of a sum [e.g., ()y^2 ] or for the

power of a difference [e.g., ()y^2 ]. Therefore, an algebraic sum or differ-

ence raised to a power cannot be simplifi ed using only rules for exponents.

Problem Simplify using only rules for exponents.

a. ()xy^2

b. ()xy+^2

c. ()xy^2

d. ()xy+^23 ()()xy+

e.

()xy

()xy

5

2

Solution

a.()y^2

Step 1. This is a power of a product, so square each factor.

()xy =xy

(^222)
P