simplify (-a)^{3/2}

Solution

simplify

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

- i a^{\frac{3}{2}}

Solution steps

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

Apply exponent rule:

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

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

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

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

= i^{3} a^{\frac{3}{2}}

i^{3} = - i

= - i a^{\frac{3}{2}}

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[\frac{y}{3} - \frac{x}{2}]^{3}