Exercise 7 Page 493

To simplify the given expression, we will use the Properties of Exponents. We will try to eliminate the exponent by splitting the terms into perfect cube factors. Let's do it!

sqrt(72x^5y^3z^8)/sqrt(3xy^2z^2)

DivSqrt

sqrt(a)/sqrt(b)=sqrt(a/b)

sqrt(72x^5y^3z^8/3xy^2z^2)

WriteProdFrac

Write as a product of fractions

sqrt(72/3 * x^5/x * y^3/y^2 * z^8/z^2)

CalcQuot

Calculate quotient

sqrt(24 * x^5/x * y^3/y^2 * z^8/z^2)

DivPow

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

sqrt(24 * x^(5-1) * y^(3-2) * z^(8-2))

SubTerms

Subtract terms

sqrt(24 * x^4 * y^1 * z^6)

ExponentOne

a^1=a

sqrt(24 * x^4 * y * z^6)

WriteProdFrac

Write as a product of fractions

sqrt(24 * x^(2 * 2) * y * z^(3 * 2))

ProdInExponent

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

sqrt(24 * (x^2)^2 * y * (z^3 )^2)

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

sqrt(24) * sqrt((x^2)^2) * sqrt(y) * sqrt((z^3 )^2)

SqrtToAbs

sqrt(a^2)=|a|

sqrt(24) * |x^2| * sqrt(y) * |z^3|

WriteProdFrac

Write as a product of fractions

sqrt(4 * 6) * |x^2| * sqrt(y) * |z^3|

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

sqrt(4) * sqrt(6) * |x^2| * sqrt(y) * |z^3|

CalcRoot

Calculate root

2 * sqrt(6) * |x^2| * sqrt(y) * |z^3|

CommutativePropMult

Commutative Property of Multiplication

2 * |x^2| * |z^3| * sqrt(6) * sqrt(y)

ProdSqrt

sqrt(a)*sqrt(b)=sqrt(a* b)

2 * |x^2| * |z^3| * sqrt(6y)

Since x^2 is a non-negative real number for exery x value, we can rewrite our expression to the simplest form. 2 * |x^2| * |z^3| * sqrt(6y) ⇕ 2 x^2|z^3| sqrt(6y) Therefore, looking at possible answers, only A corresponds well to our exercise.

Hints

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