Simplify the expression, and eliminate any negative exponent(s). a) 3x−2y59x−3y2 b) (2x3y−1y2)−2 c) (y−1x−2−1(3x−3y2)−2)

Step 1 Solve the expression: a) 3x−2y59x−3y2 Cancel the common factor: 3 x−2y53x−3y2 Apply exponent rule: xaxb=xa−b =y5x−2−(−3)3y2 Subtract the numbers: −2−(−3)=1 =xy53y2 Apply exponent rule: xaxb=xa−b =xy5−23 =xy33 Step 2 b) (2x3y−1y2)−2 Apply exponent rule: a−b=1ab =1(2x3y−1y2)2 Apply the fraction rule: 1bc=cb =y622x6 =y64x6 Step 3 c) (y−1x−2−1(3x−3y2)−2) Aplly exponent rule: a−1=1a =(3x−3y2)−21(y−1x−2) Apply exponent rule: a−b=1ab =1(y−1x−2)⋅1(3x−3y2)

Step by step solution to "Simplify the expression, and eliminate any negative exponent(s)...."

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Chesley

Answered question

2021-09-28

Simplify the expression, and eliminate any negative exponent(s).
a) $\frac{3 x^{- 2} y^{5}}{9 x^{- 3} y^{2}}$
b) ${(\frac{2 x^{3} y^{- 1}}{y^{2}})}^{- 2}$
c) $({\frac{y^{- 1}}{x^{- 2}}}^{- 1} {(\frac{3 x^{- 3}}{y^{2}})}^{- 2})$

Answer & Explanation

SoosteethicU

Skilled2021-09-29Added 102 answers

Step 1
Solve the expression:
a) $\frac{3 x^{- 2} y^{5}}{9 x^{- 3} y^{2}}$
Cancel the common factor: 3
$\frac{x^{- 2} y^{5}}{3 x^{- 3} y^{2}}$
Apply exponent rule: $\frac{x^{a}}{x^{b}} = x^{a - b}$
$= \frac{y^{5} x^{- 2 - (- 3)}}{3 y^{2}}$
Subtract the numbers: $- 2 - (- 3) = 1$
$= \frac{x y^{5}}{3 y^{2}}$
Apply exponent rule: $\frac{x^{a}}{x^{b}} = x^{a - b}$
$= \frac{x y^{5 - 2}}{3}$
$= \frac{x y^{3}}{3}$
Step 2
b) ${(\frac{2 x^{3} y^{- 1}}{y^{2}})}^{- 2}$
Apply exponent rule: $a^{- b} = \frac{1}{a^{b}}$
$= \frac{1}{{(\frac{2 x^{3} y^{- 1}}{y^{2}})}^{2}}$
Apply the fraction rule: $\frac{1}{\frac{b}{c}} = \frac{c}{b}$
$= \frac{y^{6}}{2^{2} x^{6}}$
$= \frac{y^{6}}{4 x^{6}}$
Step 3
c) $({\frac{y^{- 1}}{x^{- 2}}}^{- 1} {(\frac{3 x^{- 3}}{y^{2}})}^{- 2})$
Aplly exponent rule: $a^{- 1} = \frac{1}{a}$
$= {(\frac{3 x^{- 3}}{y^{2}})}^{- 2} \frac{1}{(\frac{y^{- 1}}{x^{- 2}})}$
Apply exponent rule: $a^{- b} = \frac{1}{a^{b}}$
$= \frac{1}{(\frac{y^{- 1}}{x^{- 2}})} \cdot \frac{1}{{(\frac{3 x^{- 3}}{y^{2}})}^{}}$

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