Simplify (64m^4)^(3/2)

${(64 m^{4})}^{\frac{3}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $64 m^{4}$ .

$64^{\frac{3}{2}} {(m^{4})}^{\frac{3}{2}}$

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

${(8^{2})}^{\frac{3}{2}} {(m^{4})}^{\frac{3}{2}}$

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

$8^{2 (\frac{3}{2})} {(m^{4})}^{\frac{3}{2}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$8^{2 (\frac{3}{2})} {(m^{4})}^{\frac{3}{2}}$

Rewrite the expression.

$8^{3} {(m^{4})}^{\frac{3}{2}}$

Step 3

Simplify the expression.

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

$512 {(m^{4})}^{\frac{3}{2}}$

Multiply the exponents in ${(m^{4})}^{\frac{3}{2}}$ .

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

$512 m^{4 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$512 m^{2 (2) \frac{3}{2}}$

Cancel the common factor.

$512 m^{2 \cdot 2 \frac{3}{2}}$

Rewrite the expression.

$512 m^{2 \cdot 3}$

Multiply $2$ by $3$ .

$512 m^{6}$