Simplify (16^(2/5)*8^(2/5))/(4^(2/5))

$\frac{16^{\frac{2}{5}} \cdot 8^{\frac{2}{5}}}{4^{\frac{2}{5}}}$

Step 1

Rewrite $16$ as $2^{4}$ .

$\frac{{(2^{4})}^{\frac{2}{5}} \cdot 8^{\frac{2}{5}}}{4^{\frac{2}{5}}}$

Step 2

Multiply the exponents in ${(2^{4})}^{\frac{2}{5}}$ .

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

$\frac{2^{4 (\frac{2}{5})} \cdot 8^{\frac{2}{5}}}{4^{\frac{2}{5}}}$

Multiply $4 (\frac{2}{5})$ .

Combine $4$ and $\frac{2}{5}$ .

$\frac{2^{\frac{4 \cdot 2}{5}} \cdot 8^{\frac{2}{5}}}{4^{\frac{2}{5}}}$

Multiply $4$ by $2$ .

$\frac{2^{\frac{8}{5}} \cdot 8^{\frac{2}{5}}}{4^{\frac{2}{5}}}$

Step 3

Rewrite $8$ as $2^{3}$ .

$\frac{2^{\frac{8}{5}} \cdot {(2^{3})}^{\frac{2}{5}}}{4^{\frac{2}{5}}}$

Step 4

Multiply the exponents in ${(2^{3})}^{\frac{2}{5}}$ .

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

$\frac{2^{\frac{8}{5}} \cdot 2^{3 (\frac{2}{5})}}{4^{\frac{2}{5}}}$

Multiply $3 (\frac{2}{5})$ .

Combine $3$ and $\frac{2}{5}$ .

$\frac{2^{\frac{8}{5}} \cdot 2^{\frac{3 \cdot 2}{5}}}{4^{\frac{2}{5}}}$

Multiply $3$ by $2$ .

$\frac{2^{\frac{8}{5}} \cdot 2^{\frac{6}{5}}}{4^{\frac{2}{5}}}$

Step 5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2^{\frac{8}{5} + \frac{6}{5}}}{4^{\frac{2}{5}}}$

Step 6

Combine the numerators over the common denominator.

$\frac{2^{\frac{8 + 6}{5}}}{4^{\frac{2}{5}}}$

Step 7

Add $8$ and $6$ .

$\frac{2^{\frac{14}{5}}}{4^{\frac{2}{5}}}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2^{\frac{14}{5}}}{4^{\frac{2}{5}}}$

Decimal Form:

$4$