Exercise 93 Page 409

We want to evaluate the given expression for the given values. Before we will substitute these values, let's simplify the given expression using Properties of Exponents. For this exercise we will begin by rearranging factors and using Product of Powers Property.

6x^(2/3)y^(1/4) * x^(- 1)y^(1/2)

SplitIntoFactors

Split into factors

6 * x^(2/3) * y^(1/4) * x^(- 1) * y^(1/2)

CommutativePropMult

Commutative Property of Multiplication

6 * x^(2/3) * x^(- 1) * y^(1/4) * y^(1/2)

MultPow

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

6 * x^(2/3 - 1) * y^(1/4 + 1/2)

▼

Simplify

NumberToFrac

a = 3* a/3

6 * x^(2/3 - 3/3) * y^(1/4 + 1/2)

ExpandFrac

a/b=a * 2/b * 2

6 * x^(2/3 - 3/3) * y^(1/4 + 2/4)

AddSubFrac

Add and subtract fractions

6 * x^(- 1/3) * y^(3/4)

Finally, we can evaluate the given expression for x=27 and y=16. To do this we should substitute these values into the expression and simplify as much as possible.

6 * x^(- 1/3) * y^(3/4)

SubstituteII

x= 27, y= 16

6 * 27^(- 1/3) * 16^(3/4)

WritePow

Write as a power

6 * ( 3^3 )^(- 1/3) * ( 2^4 )^(3/4)

▼

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

PowPow

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

6 * 3^(3 (- 1/3)) * 2^(4 (3/4))

DenomMultFracToNumber

4 * a/4= a

6 * 3^(3(- 1/3)) * 2^3

DenomMultFracToNumber

3 * a/3= a

6 * 3^(- 1) * 2^3

NegExponentToFrac

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

6 * 1/3 * 2^3

▼

Simplify

SplitIntoFactors

Split into factors

2 * 3 * 1/3 * 2^3

DenomMultFracToNumber

3 * a/3= a

2 * 1 * 2^3

IdPropMult

Identity Property of Multiplication

2 * 2^3

CalcPow

Calculate power

2 * 8

Multiply

Multiply

16