Exercise 66 Page 361

Practice makes perfect

Let's consider the given expression. 3^2 * 5^3* 8/3* 5^3 * 8 We want to simplify the expression. Let's use the Quotient of Powers Law. This law states that to divide powers with the same base, we can subtract their exponents.

3^2 * 5^3* 8/3* 5^3 * 8

CancelCommonFac

Cancel out common factors

3^2 * 5^3* 8/3* 5^3 * 8

SimpQuot

Simplify quotient

3^2 * 5^3/3* 5^3

WriteProdFrac

Write as a product of fractions

3^2/3 * 5^3/5^3

a=a^1

3^2/3^1 * 5^3/5^3

DivPow

a^m/a^n= a^(m-n)

3^(2-1)* 5^(3-3)

SubTerms

Subtract terms

3^1 * 5^0

ExponentOne

a^1=a

3 * 5^0

ExponentZero

a^0=1

3* 1

IdPropMult

Identity Property of Multiplication

We are asked to write the given algebraic expression in a simpler form. (3x)^4 Let's start by writing the expression in factored form. After doing that, we can rewrite the expression using the Commutative and Associative Properties of Multiplication.

(3x)^4

SplitIntoFactors

Split into factors

(3* x) * (3* x) * (3* x) * (3* x)

RemovePar

Remove parentheses

3* x* 3* x * 3* x * 3* x

CommutativePropMult

Commutative Property of Multiplication

3* 3 * 3* 3* x* x * x * x

AssociativePropMult

Associative Property of Multiplication

(3* 3 * 3* 3)* (x* x * x * x)

WritePow

Write as a power

(3* 3 * 3* 3)* x^4

Multiply

81x^4

Let's consider the given expression. 3^3* 3^5* (1/3)^2 We want to simplify the expression. Let's start by rewriting ( 13)^2 using the Negative Exponent Property.