2b:null 2c:["$","title",null,{"children":"Practice Exponent Laws and Rational Functions | AxiomTutor | Observable"}] 31:T540,# Practice Exponent Laws and Rational Functions ## Solutions --- ## Problem 1 Simplify ${tex`(4^{-1} x^2)^{1/2}`}. *Solution*

${tex`\frac{x}{2}`}

## Problem 2 Compute ${tex`(4\cdot 4\cdot 4)^{1/3}`}. *Solution*

## Problem 3 Simplify ${tex`(x^{-1})^{-1}`}. *Solution*

## Problem 4 Find the zeroes, holes, and asymptotes of ${tex.block`\frac{(x+1)^2(x^2+7x-18)}{x^7(x+1)}`}

Zeroes: ${tex`x=2,x=-9`}

Holes: ${tex`(-1, 0)`}

Asymptotes:
Vertical: ${tex`x=0`}
Horizontal: ${tex`y=0`}

## Problem 5 If ${tex`81^x = 1/3`} then what is *x*? *Solution*

${tex`-1/4`}

## Problem 6 If ${tex`x=y^2`} and also ${tex`y=z^3`}, then what is the value of *n* for which ${tex`x=z^n`}? *Solution*

${tex`n=4`}

## Problem 7 Assume that ${tex`\frac xy = 5`} then find the value of ${tex.block`\frac{x^2}{y^2}`} *Solution*

## Problem 8 Simplify ${tex.block`\frac{\left(\frac{7xyz^3}{2x^2y}\right)}{\left( \frac{7x^{-1}z^2}{2y^{2}}\right)}`} *Solution*

${tex.block`x^2y^{2}z`}

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