Algebra Examples

${(x y)}^{- 2} (30 x^{5}) (x y^{- 3})$

Step 1

Multiply $x^{5}$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $x$ .

${(x y)}^{- 2} (30 (x \cdot x^{5})) y^{- 3}$

Step 1.2

Multiply $x$ by $x^{5}$ .

Tap for more steps...

Step 1.2.1

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

${(x y)}^{- 2} (30 (x^{1} x^{5})) y^{- 3}$

Step 1.2.2

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

${(x y)}^{- 2} (30 x^{1 + 5}) y^{- 3}$

Step 1.3

Add $1$ and $5$ .

${(x y)}^{- 2} (30 x^{6}) y^{- 3}$

Step 2

Rewrite using the commutative property of multiplication.

$30 {(x y)}^{- 2} x^{6} y^{- 3}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$30 \frac{1}{{(x y)}^{2}} x^{6} y^{- 3}$

Step 4

Apply the product rule to $x y$ .

$30 \frac{1}{x^{2} y^{2}} x^{6} y^{- 3}$

Step 5

Combine $30$ and $\frac{1}{x^{2} y^{2}}$ .

$\frac{30}{x^{2} y^{2}} x^{6} y^{- 3}$

Step 6

Cancel the common factor of $x^{2}$ .

Tap for more steps...

Step 6.1

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

$\frac{30}{x^{2} (y^{2})} x^{6} y^{- 3}$

Step 6.2

Factor $x^{2}$ out of $x^{6}$ .

$\frac{30}{x^{2} (y^{2})} (x^{2} x^{4}) y^{- 3}$

Step 6.3

Cancel the common factor.

$\frac{30}{x^{2} y^{2}} (x^{2} x^{4}) y^{- 3}$

Step 6.4

Rewrite the expression.

$\frac{30}{y^{2}} x^{4} y^{- 3}$

Step 7

Combine $\frac{30}{y^{2}}$ and $x^{4}$ .

$\frac{30 x^{4}}{y^{2}} y^{- 3}$

Step 8

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

Tap for more steps...

Step 8.1

Factor $y^{- 3}$ out of $y^{2}$ .

$\frac{30 x^{4}}{y^{- 3} y^{5}} y^{- 3}$

Step 8.2

Cancel the common factor.

$\frac{30 x^{4}}{y^{- 3} y^{5}} y^{- 3}$

Step 8.3

Rewrite the expression.

$\frac{30 x^{4}}{y^{5}}$