Exercise 51 Page 448

Practice makes perfect

a To simplify the given expression, we will use the Properties of Rational Exponents. Start with splitting the number into the factors.

64^()13

SplitIntoFactors

Split into factors

(4*4*4)^()13

WritePow

Write as a power

(4^3)^()13

PowPow

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

4^(3* 13)

DenomMultFracToNumber

3 * a/3= a

4^1

ExponentOne

a^1=a

b We will use the Properties of Rational Exponents to simplify the given expression. Remember that when you have a negative exponent of an expression you can move it to the denominator and its exponent will become positive. Let's do it!

(4x^2y^5)^(-2)

NegExponentToFrac

a^(- m)=1/a^m

1/(4x^2y^5)^2

PowProdII

(a b)^m=a^m b^m

1/4^2(x^2)^2(y^5)^2

PowPow

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

1/4^2x^(2*2)y^(5*2)

Multiply

1/4^2x^4y^(10)

CalcPow

Calculate power

1/16x^4y^(10)

c To simplify the given expression we will use the Properties of Rational Exponents. For this exercise, we can remove the parentheses first and then combine terms with the same base.

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

RemovePar

Remove parentheses

2x^2y^(-3)3x^(-1)y^5

CommutativePropMult

Commutative Property of Multiplication

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

MultPow

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

2*3x^(2+(-1))y^(-3+5)

AddTerms

Add terms