Evaluate (256^(4/7))/(2^(4/7))

$\frac{256^{\frac{4}{7}}}{2^{\frac{4}{7}}}$

Step 1

Use the power of quotient rule $\frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m}$ .

${(\frac{256}{2})}^{\frac{4}{7}}$

Step 2

Simplify the expression.

Divide $256$ by $2$ .

$128^{\frac{4}{7}}$

Rewrite $128$ as $2^{7}$ .

${(2^{7})}^{\frac{4}{7}}$

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

$2^{7 (\frac{4}{7})}$

Step 3

Cancel the common factor of $7$ .

Cancel the common factor.

$2^{7 (\frac{4}{7})}$

Rewrite the expression.

$2^{4}$

Step 4

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

$16$