Algebra Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.4.1

Cancel the common factor.

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

Step 1.4.2

Rewrite the expression.

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

Step 1.5

Evaluate the exponent.

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

Step 1.6

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

Tap for more steps...

Step 1.6.1

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

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

Step 1.6.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.6.2.1

Cancel the common factor.

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

Step 1.6.2.2

Rewrite the expression.

$\frac{2 x^{\frac{3}{2}}}{2 x^{1}}$

Step 1.7

Simplify.

$\frac{2 x^{\frac{3}{2}}}{2 x}$

Step 2

Move $x^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{2 x^{\frac{3}{2}} x^{- 1}}{2}$

Step 3

Multiply $x^{\frac{3}{2}}$ by $x^{- 1}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $x^{- 1}$ .

$\frac{2 (x^{- 1} x^{\frac{3}{2}})}{2}$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 x^{- 1 + \frac{3}{2}}}{2}$

Step 3.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x^{- 1 \cdot \frac{2}{2} + \frac{3}{2}}}{2}$

Step 3.4

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{2 x^{\frac{- 1 \cdot 2}{2} + \frac{3}{2}}}{2}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{2 x^{\frac{- 1 \cdot 2 + 3}{2}}}{2}$

Step 3.6

Simplify the numerator.

Tap for more steps...

Step 3.6.1

Multiply $- 1$ by $2$ .

$\frac{2 x^{\frac{- 2 + 3}{2}}}{2}$

Step 3.6.2

Add $- 2$ and $3$ .

$\frac{2 x^{\frac{1}{2}}}{2}$

Step 4

Cancel the common factor.

$\frac{2 x^{\frac{1}{2}}}{2}$

Step 5

Divide $x^{\frac{1}{2}}$ by $1$ .

$x^{\frac{1}{2}}$