Simplify (2^3)^-1(4m^3)^2

${(2^{3})}^{- 1} {(4 m^{3})}^{2}$

Step 1

Multiply the exponents in ${(2^{3})}^{- 1}$ .

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

$2^{3 \cdot - 1} {(4 m^{3})}^{2}$

Multiply $3$ by $- 1$ .

$2^{- 3} {(4 m^{3})}^{2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2^{3}} {(4 m^{3})}^{2}$

Step 3

Simplify the expression.

Raise $2$ to the power of $3$ .

$\frac{1}{8} {(4 m^{3})}^{2}$

Apply the product rule to $4 m^{3}$ .

$\frac{1}{8} (4^{2} {(m^{3})}^{2})$

Raise $4$ to the power of $2$ .

$\frac{1}{8} (16 {(m^{3})}^{2})$

Step 4

Cancel the common factor of $8$ .

Factor $8$ out of $16 {(m^{3})}^{2}$ .

$\frac{1}{8} (8 (2 {(m^{3})}^{2}))$

Cancel the common factor.

$\frac{1}{8} (8 (2 {(m^{3})}^{2}))$

Rewrite the expression.

$2 {(m^{3})}^{2}$

Step 5

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

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

$2 m^{3 \cdot 2}$

Multiply $3$ by $2$ .

$2 m^{6}$