What is (3^{1/5})/(\sqrt[5]{-96)} ?

The solution to (3^{1/5})/(\sqrt[5]{-96)} is -1/2

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simplify (3^{1/5})/(\sqrt[5]{-96)}

simplify

- \frac{1}{2}

Solution steps

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= (\frac{3}{- 96})^{\frac{1}{5}}

\frac{3}{- 96} = - \frac{1}{32}

= (- \frac{1}{32})^{\frac{1}{5}}

Apply exponent rule:

(- a)^{\frac{1}{n}} = - (a)^{\frac{1}{n}},

n

is odd

(- \frac{1}{32})^{\frac{1}{5}} = - (\frac{1}{32})^{\frac{1}{5}}

= - (\frac{1}{32})^{\frac{1}{5}}

Apply radical rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}},

assuming

a \geq 0, b \geq 0

(\frac{1}{32})^{\frac{1}{5}} = \frac{1 ^{\frac{1}{5}}}{3 2 ^{\frac{1}{5}}}

= - \frac{1 ^{\frac{1}{5}}}{3 2 ^{\frac{1}{5}}}

3 2^{\frac{1}{5}} = 2

= - \frac{1 ^{\frac{1}{5}}}{2}

Apply rule

1^{a} = 1

1^{\frac{1}{5}} = 1

= - \frac{1}{2}

\frac{2 2}{3}

\frac{3 x y ^{3}}{7 x ^{2} y ^{2}} \cdot \frac{21 x y}{6 y ^{4}}

1 5^{2} + 8^{2}

2 x^{2} - x - 10 \geq 0

a^{2} + a

What is (3^{1/5})/(\sqrt[5]{-96)} ?
The solution to (3^{1/5})/(\sqrt[5]{-96)} is -1/2