Simplify (2x^-3y^3)(-7x^5y^-6)

$(2 x^{- 3} y^{3}) (- 7 x^{5} y^{- 6})$

Step 1

Multiply $x^{- 3}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$2 (x^{5} x^{- 3}) y^{3} (- 7 y^{- 6})$

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

$2 x^{5 - 3} y^{3} (- 7 y^{- 6})$

Subtract $3$ from $5$ .

$2 x^{2} y^{3} (- 7 y^{- 6})$

Step 2

Multiply $y^{3}$ by $y^{- 6}$ by adding the exponents.

Move $y^{- 6}$ .

$2 x^{2} (y^{- 6} y^{3}) \cdot - 7$

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

$2 x^{2} y^{- 6 + 3} \cdot - 7$

Add $- 6$ and $3$ .

$2 x^{2} y^{- 3} \cdot - 7$

Step 3

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

$2 x^{2} \frac{1}{y^{3}} \cdot - 7$

Step 4

Multiply $2 x^{2} \frac{1}{y^{3}}$ .

Combine $2$ and $\frac{1}{y^{3}}$ .

$x^{2} \frac{2}{y^{3}} \cdot - 7$

Combine $x^{2}$ and $\frac{2}{y^{3}}$ .

$\frac{x^{2} \cdot 2}{y^{3}} \cdot - 7$

Step 5

Move $2$ to the left of $x^{2}$ .

$\frac{2 \cdot x^{2}}{y^{3}} \cdot - 7$

Step 6

Multiply $\frac{2 x^{2}}{y^{3}} \cdot - 7$ .

Combine $\frac{2 x^{2}}{y^{3}}$ and $- 7$ .

$\frac{2 x^{2} \cdot - 7}{y^{3}}$

Multiply $- 7$ by $2$ .

$\frac{- 14 x^{2}}{y^{3}}$

Step 7

Move the negative in front of the fraction.

$- \frac{14 x^{2}}{y^{3}}$