Simplify (16a^8b^4)^(1/4)

${(16 a^{8} b^{4})}^{\frac{1}{4}}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $16 a^{8} b^{4}$ .

${(16 a^{8})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Apply the product rule to $16 a^{8}$ .

$16^{\frac{1}{4}} {(a^{8})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 2

Simplify the expression.

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

${(2^{4})}^{\frac{1}{4}} {(a^{8})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

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

$2^{4 (\frac{1}{4})} {(a^{8})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 3

Cancel the common factor of $4$ .

Cancel the common factor.

$2^{4 (\frac{1}{4})} {(a^{8})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Rewrite the expression.

$2^{1} {(a^{8})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 4

Evaluate the exponent.

$2 {(a^{8})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 5

Multiply the exponents in ${(a^{8})}^{\frac{1}{4}}$ .

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

$2 a^{8 (\frac{1}{4})} {(b^{4})}^{\frac{1}{4}}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$2 a^{4 (2) \frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Cancel the common factor.

$2 a^{4 \cdot 2 \frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Rewrite the expression.

$2 a^{2} {(b^{4})}^{\frac{1}{4}}$

Step 6

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

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

$2 a^{2} b^{4 (\frac{1}{4})}$

Cancel the common factor of $4$ .

Cancel the common factor.

$2 a^{2} b^{4 (\frac{1}{4})}$

Rewrite the expression.

$2 a^{2} b^{1}$

Step 7

Simplify.

$2 a^{2} b$