Precalculus Examples

$(5 x^{3} y^{- 3}) (- 6 x^{4} y)$

Step 1

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $x^{4}$ .

$5 (x^{4} x^{3}) y^{- 3} (- 6 y)$

Step 1.2

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

$5 x^{4 + 3} y^{- 3} (- 6 y)$

Step 1.3

Add $4$ and $3$ .

$5 x^{7} y^{- 3} (- 6 y)$

Step 2

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

Tap for more steps...

Step 2.1

Move $y$ .

$5 x^{7} (y \cdot y^{- 3}) \cdot - 6$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$5 x^{7} (y^{1} y^{- 3}) \cdot - 6$

Step 2.2.2

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

$5 x^{7} y^{1 - 3} \cdot - 6$

Step 2.3

Subtract $3$ from $1$ .

$5 x^{7} y^{- 2} \cdot - 6$

Step 3

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

$5 x^{7} \frac{1}{y^{2}} \cdot - 6$

Step 4

Multiply $5 x^{7} \frac{1}{y^{2}}$ .

Tap for more steps...

Step 4.1

Combine $5$ and $\frac{1}{y^{2}}$ .

$x^{7} \frac{5}{y^{2}} \cdot - 6$

Step 4.2

Combine $x^{7}$ and $\frac{5}{y^{2}}$ .

$\frac{x^{7} \cdot 5}{y^{2}} \cdot - 6$

Step 5

Move $5$ to the left of $x^{7}$ .

$\frac{5 \cdot x^{7}}{y^{2}} \cdot - 6$

Step 6

Multiply $\frac{5 x^{7}}{y^{2}} \cdot - 6$ .

Tap for more steps...

Step 6.1

Combine $\frac{5 x^{7}}{y^{2}}$ and $- 6$ .

$\frac{5 x^{7} \cdot - 6}{y^{2}}$

Step 6.2

Multiply $- 6$ by $5$ .

$\frac{- 30 x^{7}}{y^{2}}$

Step 7

Move the negative in front of the fraction.

$- \frac{30 x^{7}}{y^{2}}$