Simplify ((2y^(1/5))^4)/(y^(3/10))

$\frac{{(2 y^{\frac{1}{5}})}^{4}}{y^{\frac{3}{10}}}$

Step 1

Simplify the numerator.

Apply the product rule to $2 y^{\frac{1}{5}}$ .

$\frac{2^{4} {(y^{\frac{1}{5}})}^{4}}{y^{\frac{3}{10}}}$

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

$\frac{16 {(y^{\frac{1}{5}})}^{4}}{y^{\frac{3}{10}}}$

Multiply the exponents in ${(y^{\frac{1}{5}})}^{4}$ .

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

$\frac{16 y^{\frac{1}{5} \cdot 4}}{y^{\frac{3}{10}}}$

Combine $\frac{1}{5}$ and $4$ .

$\frac{16 y^{\frac{4}{5}}}{y^{\frac{3}{10}}}$

Step 2

Move $y^{\frac{3}{10}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$16 y^{\frac{4}{5}} y^{- \frac{3}{10}}$

Step 3

Multiply $y^{\frac{4}{5}}$ by $y^{- \frac{3}{10}}$ by adding the exponents.

Move $y^{- \frac{3}{10}}$ .

$16 (y^{- \frac{3}{10}} y^{\frac{4}{5}})$

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

$16 y^{- \frac{3}{10} + \frac{4}{5}}$

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$16 y^{- \frac{3}{10} + \frac{4}{5} \cdot \frac{2}{2}}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$16 y^{- \frac{3}{10} + \frac{4 \cdot 2}{5 \cdot 2}}$

Multiply $5$ by $2$ .

$16 y^{- \frac{3}{10} + \frac{4 \cdot 2}{10}}$

Combine the numerators over the common denominator.

$16 y^{\frac{- 3 + 4 \cdot 2}{10}}$

Simplify the numerator.

Multiply $4$ by $2$ .

$16 y^{\frac{- 3 + 8}{10}}$

Add $- 3$ and $8$ .

$16 y^{\frac{5}{10}}$

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $5$ .

$16 y^{\frac{5 (1)}{10}}$

Cancel the common factors.

Factor $5$ out of $10$ .

$16 y^{\frac{5 \cdot 1}{5 \cdot 2}}$

Cancel the common factor.

$16 y^{\frac{5 \cdot 1}{5 \cdot 2}}$

Rewrite the expression.

$16 y^{\frac{1}{2}}$