Algebra Examples

${(16 x^{8} y z^{12})}^{\frac{1}{4}}$

Step 1

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

Tap for more steps...

Step 1.1

Apply the product rule to $16 x^{8} y z^{12}$ .

${(16 x^{8} y)}^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 1.2

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

${(16 x^{8})}^{\frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 1.3

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

$16^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 2

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

${(2^{4})}^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 3

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

$2^{4 (\frac{1}{4})} {(x^{8})}^{\frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 4

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$2^{4 (\frac{1}{4})} {(x^{8})}^{\frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 4.2

Rewrite the expression.

$2^{1} {(x^{8})}^{\frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 5

Evaluate the exponent.

$2 {(x^{8})}^{\frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 6

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

Tap for more steps...

Step 6.1

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

$2 x^{8 (\frac{1}{4})} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 6.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.2.1

Factor $4$ out of $8$ .

$2 x^{4 (2) \frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 6.2.2

Cancel the common factor.

$2 x^{4 \cdot 2 \frac{1}{4}} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 6.2.3

Rewrite the expression.

$2 x^{2} y^{\frac{1}{4}} {(z^{12})}^{\frac{1}{4}}$

Step 7

Multiply the exponents in ${(z^{12})}^{\frac{1}{4}}$ .

Tap for more steps...

Step 7.1

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

$2 x^{2} y^{\frac{1}{4}} z^{12 (\frac{1}{4})}$

Step 7.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 7.2.1

Factor $4$ out of $12$ .

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

Step 7.2.2

Cancel the common factor.

$2 x^{2} y^{\frac{1}{4}} z^{4 \cdot 3 \frac{1}{4}}$

Step 7.2.3

Rewrite the expression.

$2 x^{2} y^{\frac{1}{4}} z^{3}$

Step 8

Reorder factors in $2 x^{2} y^{\frac{1}{4}} z^{3}$ .

$2 x^{2} z^{3} y^{\frac{1}{4}}$