Pre-Algebra Demystified

4. 
   9ab^4 6ab^2 3ab


5. 7xy3x^2 zð
   2yz^2 Þ

ANSWERS

1. 10x^2 y^2


2. 
   16a^5 b^2


3. 60x^6 y^4


4. 
   162a^3 b^7


5. 
   42x^3 y^2 z^3

Raising a Monomial to a Power

When a variable is raised to a power, the exponent of the variable is multi-

plied by the power. For example,

ðx^2 Þ^3 ¼x^2 x^2 x^2 ¼x^2 þ^2 þ^2 ¼x^6

or

ðx^2 Þ^3 ¼x^2 ^3 ¼x^6

In general (xm)n¼xmn. To raise a monomial to a power, raise the numer-

ical coefficient to the power and multiply the exponents of the variables by

the power.

EXAMPLE

Find (5x^3 y^4 )^2.

SOLUTION

ð5x^3 y^4 Þ^2 ¼ 52 x^3 ^2 y^4 ^2

¼25x^6 y^8

EXAMPLE

Find (
6a^4 b^5 )^3.

238 CHAPTER 12 Monomials and Polynomials