Exercise 133 Page 437

Practice makes perfect

We are asked to simplify the given algebraic expression. (3x)^4 x^3 Let's start by writing the expression in factored form. Then, we will rewrite the expression using the Commutative and Associative Properties of Multiplication.

(3x)^4 x^3

SplitIntoFactors

Split into factors

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

RemovePar

Remove parentheses

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

CommutativePropMult

Commutative Property of Multiplication

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

AssociativePropMult

Associative Property of Multiplication

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

WritePow

Write as a power

(3* 3 * 3* 3)* x^7

Multiply

81 x^7

Let's consider the given expression. 2^4* 3/2^3* 3^2 We want to simplify the expression. We can do this by using the Quotient of Powers Law. This law states that to divide powers with the same base, we can subtract their exponents.

2^4* 3/2^3* 3^2

WriteProdFrac

Write as a product of fractions

2^4/2^3 * 3/3^2

a=a^1

2^4/2^3 * 3^1/3^2

DivPow

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

2^(4-3)* 3^(1-2)

SubTerms

Subtract terms

2^1* 3^(- 1)

ExponentOne

a^1=a

2 * 3^(- 1)

To give the answer without negative exponents, we will use the Negative Exponent Property.

Negative Exponent Property
a^(- n)=1/a^n, for every nonzero number a

Let's rewrite our expression using this property.

2 * 3^(- 1)

NegOneExponentToFrac

a^(- 1)=1/a

2* 1/3

MoveLeftFacToNumOne

a* 1/b= a/b

2/3

We want to simplify the given expression. 4^(- 3)* 4^2To do so, we will use the Product of Powers Law. This law states that to multiply powers with the same base, we can add their exponents.

4^(- 3)* 4^2

MultPow

a^m*a^n=a^(m+n)

4^(- 3+2)

AddTerms

Add terms

4^(- 1)

Next, let's rewrite our expression using the Negative Exponent Property.

4^(- 1)

NegOneExponentToFrac

a^(- 1)=1/a

1/4

Hints

Check the answer

Practice exercises

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