Precalculus Examples

$\frac{\sqrt{192 x^{3}}}{\sqrt{6 x^{- 7}}}$

Step 1

Combine $\sqrt{192 x^{3}}$ and $\sqrt{6 x^{- 7}}$ into a single radical.

$\sqrt{\frac{192 x^{3}}{6 x^{- 7}}}$

Step 2

Reduce the expression $\frac{192 x^{3}}{6 x^{- 7}}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $6$ out of $192 x^{3}$ .

$\sqrt{\frac{6 (32 x^{3})}{6 x^{- 7}}}$

Step 2.2

Factor $6$ out of $6 x^{- 7}$ .

$\sqrt{\frac{6 (32 x^{3})}{6 (x^{- 7})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{6 (32 x^{3})}{6 x^{- 7}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{32 x^{3}}{x^{- 7}}}$

Step 3

Move $x^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt{32 x^{3} x^{7}}$

Step 4

Multiply $x^{3}$ by $x^{7}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $x^{7}$ .

$\sqrt{32 (x^{7} x^{3})}$

Step 4.2

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

$\sqrt{32 x^{7 + 3}}$

Step 4.3

Add $7$ and $3$ .

$\sqrt{32 x^{10}}$

Step 5

Rewrite $32 x^{10}$ as ${(4 x^{5})}^{2} \cdot 2$ .

Tap for more steps...

Step 5.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{10}}$

Step 5.2

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

$\sqrt{4^{2} \cdot 2 x^{10}}$

Step 5.3

Rewrite $x^{10}$ as ${(x^{5})}^{2}$ .

$\sqrt{4^{2} \cdot 2 {(x^{5})}^{2}}$

Step 5.4

Move $2$ .

$\sqrt{4^{2} {(x^{5})}^{2} \cdot 2}$

Step 5.5

Rewrite $4^{2} {(x^{5})}^{2}$ as ${(4 x^{5})}^{2}$ .

$\sqrt{{(4 x^{5})}^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$4 x^{5} \sqrt{2}$