Simplify ((16y^5)/(4y^3))^(1/2)

${(\frac{16 y^{5}}{4 y^{3}})}^{\frac{1}{2}}$

Step 1

Cancel the common factor of $16$ and $4$ .

Factor $4$ out of $16 y^{5}$ .

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

Cancel the common factors.

Factor $4$ out of $4 y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Cancel the common factor of $y^{5}$ and $y^{3}$ .

Factor $y^{3}$ out of $4 y^{5}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $4 y^{2}$ by $1$ .

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

Step 3

Simplify the expression.

Apply the product rule to $4 y^{2}$ .

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

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

${(2^{2})}^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}$

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

$2^{2 (\frac{1}{2})} {(y^{2})}^{\frac{1}{2}}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2^{2 (\frac{1}{2})} {(y^{2})}^{\frac{1}{2}}$

Rewrite the expression.

$2^{1} {(y^{2})}^{\frac{1}{2}}$

Step 5

Evaluate the exponent.

$2 {(y^{2})}^{\frac{1}{2}}$

Step 6

Multiply the exponents in ${(y^{2})}^{\frac{1}{2}}$ .

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

$2 y^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 y^{2 (\frac{1}{2})}$

Rewrite the expression.

$2 y^{1}$

Step 7

Simplify.

$2 y$

Simplify ((16y^5)/(4y^3))^(1/2)

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