IMathAS-libretexts

Radical Equations and Rational Exponents
$\displaystyle {\sqrt[{{5}}]{{-{105}}}}={\left(-{105}\right)}^{{\frac{{1}}{{5}}}}$ Calculator Entry: -105^(1/5) $\displaystyle {\left({\sqrt[{{3}}]{{{49}}}}\right)}^{{2}}={49}^{{\frac{{2}}{{3}}}}$ Calculator Entry: 49^(2/3) $\displaystyle {\sqrt[{{4}}]{{{256}}}}={256}^{{\frac{{1}}{{4}}}}$ Calculator Entry: 256^1/4 $\displaystyle -{\sqrt[{{4}}]{{{34}^{{3}}}}}=-{34}^{{\frac{{3}}{{4}}}}$ Calculator Entry: -34^(3/4) $\displaystyle {\sqrt[{{3}}]{{-{125}}}}={\left(-{125}\right)}^{{\frac{{1}}{{3}}}}$ Calculator Entry: (-125)^(1/3)

Radical Equations and Rational Exponents

The following examples show how to write Radical Equations using Rational Exponents and how to enter those equations into the calculator. Which of the statements are correct? Check all that apply.

$\displaystyle {\sqrt[{{5}}]{{-{105}}}}={\left(-{105}\right)}^{{\frac{{1}}{{5}}}}$

Calculator Entry: -105^(1/5)
$\displaystyle {\left({\sqrt[{{3}}]{{{49}}}}\right)}^{{2}}={49}^{{\frac{{2}}{{3}}}}$

Calculator Entry: 49^(2/3)
$\displaystyle {\sqrt[{{4}}]{{{256}}}}={256}^{{\frac{{1}}{{4}}}}$

Calculator Entry: 256^1/4
$\displaystyle -{\sqrt[{{4}}]{{{34}^{{3}}}}}=-{34}^{{\frac{{3}}{{4}}}}$

Calculator Entry: -34^(3/4)
$\displaystyle {\sqrt[{{3}}]{{-{125}}}}={\left(-{125}\right)}^{{\frac{{1}}{{3}}}}$

Calculator Entry: (-125)^(1/3)

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