Simplify and express the final result using positive exponents. (x^{-3}y

Anonym 2021-09-29 Answered
Simplify and express the final result using positive exponents.
\(\displaystyle{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}\)

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Expert Answer

Aniqa O'Neill
Answered 2021-09-30 Author has 12976 answers
To simplify the expression: \(\displaystyle{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}\)
Solution:
Given expression is: \(\displaystyle{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}\)
On simplifying further we get:
\(\displaystyle{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}={\left({x}^{{-{3}}}\right)}^{{-{2}}}\cdot{\left({y}^{{4}}\right)}^{{-{2}}}\)
\(\displaystyle={\left({x}^{{{\left(-{3}\right)}{\left(-{2}\right)}}}\right)}{\left({y}^{{{4}{\left(-{2}\right)}}}\right)}\)
\(\displaystyle={\left({x}^{{6}}\right)}{\left({y}^{{-{8}}}\right)}\)
\(\displaystyle={\left({x}^{{6}}\right)}{\left({\frac{{{1}}}{{{y}^{{8}}}}}\right)}\)
\(\displaystyle={\left({\frac{{{x}^{{6}}}}{{{y}^{{8}}}}}\right)}\)
\(\displaystyle\Rightarrow{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}={\left({\frac{{{x}^{{6}}}}{{{y}^{{8}}}}}\right)}\)
Result: \(\displaystyle{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}={\left({\frac{{{x}^{{6}}}}{{{y}^{{8}}}}}\right)}\)
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