Pre-Algebra Examples

$\frac{\sqrt[4]{112 x^{21} y^{25}}}{7 x y^{- 2}}$

Step 1

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\sqrt[4]{112 x^{21} y^{25}} y^{2}}{7 x}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $112 x^{21} y^{25}$ as ${(2 x^{5} y^{6})}^{4} \cdot (7 x y)$ .

Tap for more steps...

Step 2.1.1

Factor $16$ out of $112$ .

$\frac{\sqrt[4]{16 (7) x^{21} y^{25}} y^{2}}{7 x}$

Step 2.1.2

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

$\frac{\sqrt[4]{2^{4} \cdot 7 x^{21} y^{25}} y^{2}}{7 x}$

Step 2.1.3

Factor out $x^{20}$ .

$\frac{\sqrt[4]{2^{4} \cdot 7 (x^{20} x) y^{25}} y^{2}}{7 x}$

Step 2.1.4

Rewrite $x^{20}$ as ${(x^{5})}^{4}$ .

$\frac{\sqrt[4]{2^{4} \cdot 7 ({(x^{5})}^{4} x) y^{25}} y^{2}}{7 x}$

Step 2.1.5

Factor out $y^{24}$ .

$\frac{\sqrt[4]{2^{4} \cdot 7 ({(x^{5})}^{4} x) (y^{24} y)} y^{2}}{7 x}$

Step 2.1.6

Rewrite $y^{24}$ as ${(y^{6})}^{4}$ .

$\frac{\sqrt[4]{2^{4} \cdot 7 ({(x^{5})}^{4} x) ({(y^{6})}^{4} y)} y^{2}}{7 x}$

Step 2.1.7

Move $x$ .

$\frac{\sqrt[4]{2^{4} \cdot 7 ({(x^{5})}^{4}) {(y^{6})}^{4} x y} y^{2}}{7 x}$

Step 2.1.8

Move $7$ .

$\frac{\sqrt[4]{(2^{4} ({(x^{5})}^{4})) {(y^{6})}^{4} \cdot 7 x y} y^{2}}{7 x}$

Step 2.1.9

Rewrite $(2^{4} ({(x^{5})}^{4})) {(y^{6})}^{4}$ as ${(2 x^{5} y^{6})}^{4}$ .

$\frac{\sqrt[4]{{(2 x^{5} y^{6})}^{4} \cdot 7 x y} y^{2}}{7 x}$

Step 2.1.10

Add parentheses.

$\frac{\sqrt[4]{{(2 x^{5} y^{6})}^{4} \cdot 7 (x y)} y^{2}}{7 x}$

Step 2.1.11

Add parentheses.

$\frac{\sqrt[4]{{(2 x^{5} y^{6})}^{4} \cdot (7 x y)} y^{2}}{7 x}$

Step 2.2

Pull terms out from under the radical.

$\frac{2 x^{5} y^{6} \sqrt[4]{7 x y} y^{2}}{7 x}$

Step 2.3

Multiply $y^{6}$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 2.3.1

Move $y^{2}$ .

$\frac{2 x^{5} (y^{2} y^{6}) \sqrt[4]{7 x y}}{7 x}$

Step 2.3.2

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

$\frac{2 x^{5} y^{2 + 6} \sqrt[4]{7 x y}}{7 x}$

Step 2.3.3

Add $2$ and $6$ .

$\frac{2 x^{5} y^{8} \sqrt[4]{7 x y}}{7 x}$

Step 3

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

Tap for more steps...

Step 3.1

Factor $x$ out of $2 x^{5} y^{8} \sqrt[4]{7 x y}$ .

$\frac{x (2 x^{4} y^{8} \sqrt[4]{7 x y})}{7 x}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $x$ out of $7 x$ .

$\frac{x (2 x^{4} y^{8} \sqrt[4]{7 x y})}{x \cdot 7}$

Step 3.2.2

Cancel the common factor.

$\frac{x (2 x^{4} y^{8} \sqrt[4]{7 x y})}{x \cdot 7}$

Step 3.2.3

Rewrite the expression.

$\frac{2 x^{4} y^{8} \sqrt[4]{7 x y}}{7}$