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Popular >

simplify (-3125)^{1/5}

Solution

simplify

(- 3125)^{\frac{1}{5}}

Solution

- 5

Solution steps

(- 3125)^{\frac{1}{5}}

Apply exponent rule:

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

if

n

is odd

(- 3125)^{\frac{1}{5}} = - 312 5^{\frac{1}{5}}

= - 312 5^{\frac{1}{5}}

Factor the number:

3125 = 5^{5}

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

Apply exponent rule:

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

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

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

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

= - 5^{1}

Apply exponent rule:

a^{1} = a

5^{1} = 5

= - 5

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Frequently Asked Questions (FAQ)

What is (-3125)^{1/5} ?
The solution to (-3125)^{1/5} is -5