Using the rules for exponents, simplify the following, (a−1b2)−1(a2)3b3b4

Given expression is (a−1b2)−1(a2)3b3b4 To simplify the given expression using the rules for exponents. Solution: Rules of exponents are: 1. (xm)n=xmn 2, xm⋅xn=xm+n 3. xmxn=xm−n Simplifying the given expression using the above rules. (a−1b2)−1(a2)3b3b4=(a−1)−1(b2)−1⋅a2−3b3b4 =a−1−1b−2⋅a6b3+4 =ab2⋅a6b7 =ab2⋅a6b−7 =a1+6b2−7 =a7b−5 =a7b5 Hence, simplified form of the expression is a7b5

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High School
Algebra
Algebra I
Exponents and radicals

Lewis Harvey

Answered question

2021-10-17

Using the rules for exponents, simplify the following,

{(\frac{a^{- 1}}{b^{2}})}^{- 1} \frac{{(a^{2})}^{3}}{b^{3} b^{4}}

Answer & Explanation

Pohanginah

Skilled2021-10-18Added 96 answers

Given expression is

{(\frac{a^{- 1}}{b^{2}})}^{- 1} \frac{{(a^{2})}^{3}}{b^{3} b^{4}}

To simplify the given expression using the rules for exponents.
Solution:
Rules of exponents are:
1.

{(x^{m})}^{n} = x^{m n}

x^{m} \cdot x^{n} = x^{m + n}

\frac{x^{m}}{x^{n}} = x^{m - n}

Simplifying the given expression using the above rules.

{(\frac{a^{- 1}}{b^{2}})}^{- 1} \frac{{(a^{2})}^{3}}{b^{3} b^{4}} = \frac{{(a^{- 1})}^{- 1}}{{(b^{2})}^{- 1}} \cdot \frac{a^{2 - 3}}{b^{3} b^{4}}

= \frac{a^{- 1 - 1}}{b^{- 2}} \cdot \frac{a^{6}}{b^{3 + 4}}

= a b^{2} \cdot \frac{a^{6}}{b^{7}}

= a b^{2} \cdot a^{6} b^{- 7}

= a^{1 + 6} b^{2 - 7}

= a^{7} b^{- 5}

= \frac{a^{7}}{b^{5}}

Hence, simplified form of the expression is

\frac{a^{7}}{b^{5}}

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