To simplify the expression (-27)^{\frac{1}{3}}

usagirl007A 2021-11-07 Answered
To simplify the expression \(\displaystyle{\left(-{27}\right)}^{{{\frac{{{1}}}{{{3}}}}}}\)

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Expert Answer

Aubree Mcintyre
Answered 2021-11-08 Author has 18011 answers
Step 1
According to the power rule \(\displaystyle{\left({b}^{{{n}}}\right)}{m}={b}^{{{n}}}\cdot{m}\)
Given expression is \(\displaystyle{\left(-{27}\right)}^{{{\frac{{{1}}}{{{3}}}}}}\)
This can be written as \(\displaystyle{\left(-{27}\right)}^{{{\frac{{{1}}}{{{3}}}}}}={\left\lbrace{\left(-{3}\right)}\times{\left(-{3}\right)}\times{\left(-{3}\right)}\right\rbrace}^{{{\frac{{{1}}}{{{3}}}}}}\)
\(\displaystyle{\left(-{27}\right)}^{{{\frac{{{1}}}{{{3}}}}}}={\left\lbrace{\left(-{3}\right)}^{{{3}}}\right\rbrace}^{{{\frac{{{1}}}{{{3}}}}}}\)
Applying the power rule,
\(\displaystyle{\left(-{27}\right)}^{{{\frac{{{1}}}{{{3}}}}}}={\left\lbrace{\left(-{3}\right)}\right\rbrace}^{{{3}\times{\frac{{{1}}}{{{3}}}}}}\)
\(\displaystyle{\left(-{27}\right)}^{{{\frac{{{1}}}{{{3}}}}}}={\left(-{3}\right)}\)
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