Evaluate -64^(3/2)

$- 64^{\frac{3}{2}}$

Step 1

Simplify the expression.

Rewrite $64$ as $8^{2}$ .

$- {(8^{2})}^{\frac{3}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 8^{2 (\frac{3}{2})}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$- 8^{2 (\frac{3}{2})}$

Rewrite the expression.

$- 8^{3}$

Step 3

Simplify the expression.

Raise $8$ to the power of $3$ .

$- 1 \cdot 512$

Multiply $- 1$ by $512$ .

$- 512$