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Popular >

simplify (-2)^{3/2}

Solution

simplify

(- 2)^{\frac{3}{2}}

Solution

- 2 \cdot 2^{\frac{1}{2}} i

Solution steps

(- 2)^{\frac{3}{2}}

Apply exponent rule:

a^{\frac{m}{n}} = (a^{\frac{1}{n}})^{m}

(- 2)^{\frac{3}{2}} = ((- 2)^{\frac{1}{2}})^{3}

= ((- 2)^{\frac{1}{2}})^{3}

(- 2)^{\frac{1}{2}} = 2 i

= (2 i)^{3}

Simplify

(2 i)^{3} : - 2 \cdot 2^{\frac{1}{2}} i

= - 2 \cdot 2^{\frac{1}{2}} i

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Frequently Asked Questions (FAQ)

What is (-2)^{3/2} ?
The solution to (-2)^{3/2} is -2*2^{1/2}i