Algebra Examples

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

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 $x^{\frac{1}{8}} y^{\frac{1}{4}} z^{\frac{1}{2}}$ .

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

Step 1.2

Apply the product rule to $x^{\frac{1}{8}} y^{\frac{1}{4}}$ .

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 3

Simplify.

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

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.2.1

Factor $4$ out of $8$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Multiply the exponents in ${(z^{\frac{1}{2}})}^{8}$ .

Tap for more steps...

Step 5.1

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

$x y^{2} z^{\frac{1}{2} \cdot 8}$

Step 5.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1

Factor $2$ out of $8$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$x y^{2} z^{4}$