Algebra Examples

$\frac{5 x^{- 1} y^{\frac{1}{2}}}{\sqrt{25 x^{4} y^{2}}}$

Step 1

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

$\frac{5 y^{\frac{1}{2}}}{\sqrt{25 x^{4} y^{2}} x}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $25 x^{4} y^{2}$ as ${(5 x^{2} y)}^{2}$ .

$\frac{5 y^{\frac{1}{2}}}{\sqrt{{(5 x^{2} y)}^{2}} x}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{5 y^{\frac{1}{2}}}{5 x^{2} y x}$

Step 2.3

Combine exponents.

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Step 2.3.1

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

$\frac{5 y^{\frac{1}{2}}}{5 (x^{1} x^{2}) y}$

Step 2.3.2

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

$\frac{5 y^{\frac{1}{2}}}{5 x^{1 + 2} y}$

Step 2.3.3

Add $1$ and $2$ .

$\frac{5 y^{\frac{1}{2}}}{5 x^{3} y}$

Step 3

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

$\frac{5}{5 x^{3} y \cdot y^{- \frac{1}{2}}}$

Step 4

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

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Step 4.1

Move $y^{- \frac{1}{2}}$ .

$\frac{5}{5 x^{3} (y^{- \frac{1}{2}} y)}$

Step 4.2

Multiply $y^{- \frac{1}{2}}$ by $y$ .

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Step 4.2.1

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

$\frac{5}{5 x^{3} (y^{- \frac{1}{2}} y^{1})}$

Step 4.2.2

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

$\frac{5}{5 x^{3} y^{- \frac{1}{2} + 1}}$

Step 4.3

Write $1$ as a fraction with a common denominator.

$\frac{5}{5 x^{3} y^{- \frac{1}{2} + \frac{2}{2}}}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{5}{5 x^{3} y^{\frac{- 1 + 2}{2}}}$

Step 4.5

Add $- 1$ and $2$ .

$\frac{5}{5 x^{3} y^{\frac{1}{2}}}$

Step 5

Cancel the common factor.

$\frac{5}{5 x^{3} y^{\frac{1}{2}}}$

Step 6

Rewrite the expression.

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