Simplify -3x^-7y*x^5y^-3

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

Step 1

Multiply $x^{- 7}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

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

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

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

Subtract $7$ from $5$ .

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

Step 2

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

Move $y^{- 3}$ .

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

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

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

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

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

$- 3 x^{- 2} y^{- 3 + 1}$

Add $- 3$ and $1$ .

$- 3 x^{- 2} y^{- 2}$

Step 3

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

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

Step 4

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

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

Step 5

Move the negative in front of the fraction.

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

Step 6

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

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

Step 7

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

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