Algebra Examples

${(\frac{128 x^{5}}{8 x})}^{\frac{1}{4}}$

Step 1

Cancel the common factor of $128$ and $8$ .

Tap for more steps...

Step 1.1

Factor $8$ out of $128 x^{5}$ .

${(\frac{8 (16 x^{5})}{8 x})}^{\frac{1}{4}}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $8$ out of $8 x$ .

${(\frac{8 (16 x^{5})}{8 (x)})}^{\frac{1}{4}}$

Step 1.2.2

Cancel the common factor.

${(\frac{8 (16 x^{5})}{8 x})}^{\frac{1}{4}}$

Step 1.2.3

Rewrite the expression.

${(\frac{16 x^{5}}{x})}^{\frac{1}{4}}$

Step 2

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

Tap for more steps...

Step 2.1

Factor $x$ out of $16 x^{5}$ .

${(\frac{x (16 x^{4})}{x})}^{\frac{1}{4}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Raise $x$ to the power of $1$ .

${(\frac{x (16 x^{4})}{x^{1}})}^{\frac{1}{4}}$

Step 2.2.2

Factor $x$ out of $x^{1}$ .

${(\frac{x (16 x^{4})}{x \cdot 1})}^{\frac{1}{4}}$

Step 2.2.3

Cancel the common factor.

${(\frac{x (16 x^{4})}{x \cdot 1})}^{\frac{1}{4}}$

Step 2.2.4

Rewrite the expression.

${(\frac{16 x^{4}}{1})}^{\frac{1}{4}}$

Step 2.2.5

Divide $16 x^{4}$ by $1$ .

${(16 x^{4})}^{\frac{1}{4}}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Apply the product rule to $16 x^{4}$ .

$16^{\frac{1}{4}} {(x^{4})}^{\frac{1}{4}}$

Step 3.2

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

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

Step 3.3

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

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

Step 4

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Evaluate the exponent.

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

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.2.1

Cancel the common factor.

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

Step 6.2.2

Rewrite the expression.

$2 x^{1}$

Step 7

Simplify.

$2 x$