Exercise 136 Page 384

We want to rewrite the given expression in a simpler form. 3^2* 3^5 Let's use the Product of Powers Law. This law states that to multiply powers with the same base, we can add their exponents.

3^2* 3^5

MultPow

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

3^(2+5)

AddTerms

Add terms

3^7

Let's consider the given expression. 4^5/4^3 We are asked to write the expression in a simpler form. To do this, we can use the Quotient of Powers Law. This law states that to divide powers with the same base, we can subtract their exponents.

4^5/4^3

DivPow

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

4^(5-3)

SubTerm

Subtract term

4^2

We are asked to write the given algebraic expression in a simpler form. (3x^2)^4 Let's start by writing the expression in the factored form. Then, we will rewrite the expression using the Commutative and Associative Properties of Multiplication.

(3x^2)^4

PowToProdTwoFac

a^2=a* a

(3* x* x)^4

SplitIntoFactors

Split into factors

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

RemovePar

Remove parentheses

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

CommutativePropMult

Commutative Property of Multiplication

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

AssociativePropMult

Associative Property of Multiplication

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

WritePow

Write as a power

(3* 3 * 3* 3)* x^8

Multiply

81x^8

Let's analyze the given expression. (3x^3)(7x^5) To rewrite the expression in a simpler form, we will use the Product of Powers Law. In this case, we will also use the Commutative and Associative Properties of Multiplication. Let's do it!

(3x^3)(7x^5)

RemovePar

Remove parentheses

3x^3* 7x^5

CommutativePropMult

Commutative Property of Multiplication

3* 7* x^3* x^5

Multiply

21* x^3* x^5

MultPow

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

21* x^(3+5)