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Popular >

simplify (-243)^{1/5}

Solution

simplify

(- 243)^{\frac{1}{5}}

Solution

- 3

Solution steps

(- 243)^{\frac{1}{5}}

Apply exponent rule:

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

if

n

is odd

(- 243)^{\frac{1}{5}} = - 24 3^{\frac{1}{5}}

= - 24 3^{\frac{1}{5}}

Factor the number:

243 = 3^{5}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(3^{5})^{\frac{1}{5}} = 3^{5 \cdot \frac{1}{5}}

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

5 \cdot \frac{1}{5} = 1

= - 3^{1}

Apply exponent rule:

a^{1} = a

3^{1} = 3

= - 3

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Frequently Asked Questions (FAQ)

What is (-243)^{1/5} ?
The solution to (-243)^{1/5} is -3