Find out the answer to "Simplify and express the final result using positive..."

York

Answered question

2021-10-21

Simplify and express the final result using positive exponents.

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

Alix Ortiz

Skilled2021-10-22Added 109 answers

To simplify:
The expression

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

and express the result in positive exponents.
Concept used:
Exponent rule:

a^{- m} = \frac{1}{a^{m}}

{(\frac{a}{b})}^{- m} = {(\frac{b}{a})}^{m}

{(a^{m})}^{n} = a^{m \times n}

Calculation:
The simplifacation of

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

can be obtained as,

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

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

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

= (\frac{27 a^{3} b^{12}}{8})

Thus, the simplified form of the expression

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

\frac{27 a^{3} b^{12}}{8}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?