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Popular >

simplify (-125)^{1/3}

Solution

simplify

(- 125)^{\frac{1}{3}}

Solution

- 5

Solution steps

(- 125)^{\frac{1}{3}}

Apply exponent rule:

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

if

n

is odd

(- 125)^{\frac{1}{3}} = - 12 5^{\frac{1}{3}}

= - 12 5^{\frac{1}{3}}

Factor the number:

125 = 5^{3}

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

Apply exponent rule:

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

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

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

3 \cdot \frac{1}{3} = 1

= - 5^{1}

Apply exponent rule:

a^{1} = a

5^{1} = 5

= - 5

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Frequently Asked Questions (FAQ)

What is (-125)^{1/3} ?
The solution to (-125)^{1/3} is -5