Algebra Examples

${(\frac{5^{2} x^{3} y^{- 3}}{125 x y})}^{- 1}$

Step 1

Move $y^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{5^{2} x^{3}}{125 x y \cdot y^{3}})}^{- 1}$

Step 2

Multiply $y$ by $y^{3}$ by adding the exponents.

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Step 2.1

Move $y^{3}$ .

${(\frac{5^{2} x^{3}}{125 x (y^{3} y)})}^{- 1}$

Step 2.2

Multiply $y^{3}$ by $y$ .

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Step 2.2.1

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

${(\frac{5^{2} x^{3}}{125 x (y^{3} y^{1})})}^{- 1}$

Step 2.2.2

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

${(\frac{5^{2} x^{3}}{125 x y^{3 + 1}})}^{- 1}$

Step 2.3

Add $3$ and $1$ .

${(\frac{5^{2} x^{3}}{125 x y^{4}})}^{- 1}$

Step 3

Cancel the common factor of $x^{3}$ and $x$ .

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Step 3.1

Factor $x$ out of $5^{2} x^{3}$ .

${(\frac{x (5^{2} x^{2})}{125 x y^{4}})}^{- 1}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $125 x y^{4}$ .

${(\frac{x (5^{2} x^{2})}{x (125 y^{4})})}^{- 1}$

Step 3.2.2

Cancel the common factor.

${(\frac{x (5^{2} x^{2})}{x (125 y^{4})})}^{- 1}$

Step 3.2.3

Rewrite the expression.

${(\frac{5^{2} x^{2}}{125 y^{4}})}^{- 1}$

Step 4

Raise $5$ to the power of $2$ .

${(\frac{25 x^{2}}{125 y^{4}})}^{- 1}$

Step 5

Cancel the common factor of $25$ and $125$ .

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Step 5.1

Factor $25$ out of $25 x^{2}$ .

${(\frac{25 (x^{2})}{125 y^{4}})}^{- 1}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $25$ out of $125 y^{4}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

${(\frac{x^{2}}{5 y^{4}})}^{- 1}$

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{5 y^{4}}{x^{2}}$