Precalculus Examples

${(\frac{25 x^{3} y^{3}}{x y})}^{\frac{3}{2}}$

Step 1

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

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Step 1.1

Factor $x$ out of $25 x^{3} y^{3}$ .

${(\frac{x (25 x^{2} y^{3})}{x y})}^{\frac{3}{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x$ out of $x y$ .

${(\frac{x (25 x^{2} y^{3})}{x (y)})}^{\frac{3}{2}}$

Step 1.2.2

Cancel the common factor.

${(\frac{x (25 x^{2} y^{3})}{x y})}^{\frac{3}{2}}$

Step 1.2.3

Rewrite the expression.

${(\frac{25 x^{2} y^{3}}{y})}^{\frac{3}{2}}$

Step 2

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

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Step 2.1

Factor $y$ out of $25 x^{2} y^{3}$ .

${(\frac{y (25 x^{2} y^{2})}{y})}^{\frac{3}{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

${(\frac{y (25 x^{2} y^{2})}{y^{1}})}^{\frac{3}{2}}$

Step 2.2.2

Factor $y$ out of $y^{1}$ .

${(\frac{y (25 x^{2} y^{2})}{y \cdot 1})}^{\frac{3}{2}}$

Step 2.2.3

Cancel the common factor.

${(\frac{y (25 x^{2} y^{2})}{y \cdot 1})}^{\frac{3}{2}}$

Step 2.2.4

Rewrite the expression.

${(\frac{25 x^{2} y^{2}}{1})}^{\frac{3}{2}}$

Step 2.2.5

Divide $25 x^{2} y^{2}$ by $1$ .

${(25 x^{2} y^{2})}^{\frac{3}{2}}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $25 x^{2} y^{2}$ .

${(25 x^{2})}^{\frac{3}{2}} {(y^{2})}^{\frac{3}{2}}$

Step 3.2

Apply the product rule to $25 x^{2}$ .

$25^{\frac{3}{2}} {(x^{2})}^{\frac{3}{2}} {(y^{2})}^{\frac{3}{2}}$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $25$ as $5^{2}$ .

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

Step 4.2

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

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

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

Simplify the expression.

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Step 6.1

Raise $5$ to the power of $3$ .

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

Step 6.2

Multiply the exponents in ${(x^{2})}^{\frac{3}{2}}$ .

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Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor of $2$ .

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Step 6.2.2.1

Cancel the common factor.

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

Step 6.2.2.2

Rewrite the expression.

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

Step 6.3

Multiply the exponents in ${(y^{2})}^{\frac{3}{2}}$ .

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Step 6.3.1

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

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

Step 6.3.2

Cancel the common factor of $2$ .

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Step 6.3.2.1

Cancel the common factor.

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

Step 6.3.2.2

Rewrite the expression.

$125 x^{3} y^{3}$