Algebra Examples

$\frac{{(3 x)}^{- 3} y^{4}}{- x^{2} y^{- 6}}$

Step 1

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

$\frac{y^{4}}{- x^{2} y^{- 6} {(3 x)}^{3}}$

Step 2

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{y^{4} y^{6}}{- x^{2} {(3 x)}^{3}}$

Step 3

Multiply $y^{4}$ by $y^{6}$ by adding the exponents.

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Step 3.1

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

$\frac{y^{4 + 6}}{- x^{2} {(3 x)}^{3}}$

Step 3.2

Add $4$ and $6$ .

$\frac{y^{10}}{- x^{2} {(3 x)}^{3}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $3 x$ .

$\frac{y^{10}}{- x^{2} \cdot 3^{3} x^{3}}$

Step 4.2

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 4.2.1

Move $x^{3}$ .

$\frac{y^{10}}{- (x^{3} x^{2}) \cdot 3^{3}}$

Step 4.2.2

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

$\frac{y^{10}}{- x^{3 + 2} \cdot 3^{3}}$

Step 4.2.3

Add $3$ and $2$ .

$\frac{y^{10}}{- x^{5} \cdot 3^{3}}$

Step 4.3

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

$\frac{y^{10}}{- x^{5} \cdot 27}$

Step 4.4

Multiply $27$ by $- 1$ .

$\frac{y^{10}}{- 27 x^{5}}$

Step 5

Move the negative in front of the fraction.

$- \frac{y^{10}}{27 x^{5}}$