Trigonometry Examples

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

Step 1

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

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

Step 2

Move ${(x y^{4})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

${(\frac{x \cdot x^{2} y^{4}}{y^{3}})}^{5}$

Step 3.2

Multiply $x$ by $x^{2}$ .

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $2$ .

${(\frac{x^{3} y^{4}}{y^{3}})}^{5}$

Step 4

Cancel the common factor of $y^{4}$ and $y^{3}$ .

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Step 4.1

Factor $y^{3}$ out of $x^{3} y^{4}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.2.4

Divide $x^{3} y$ by $1$ .

${(x^{3} y)}^{5}$

Step 5

Apply basic rules of exponents.

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Step 5.1

Apply the product rule to $x^{3} y$ .

${(x^{3})}^{5} y^{5}$

Step 5.2

Multiply the exponents in ${(x^{3})}^{5}$ .

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Step 5.2.1

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

$x^{3 \cdot 5} y^{5}$

Step 5.2.2

Multiply $3$ by $5$ .

$x^{15} y^{5}$