Simplify (8x^4y^-3)(1/2x^-5y^2)

$(8 x^{4} y^{- 3}) (\frac{1}{2} x^{- 5} y^{2})$

Step 1

Multiply $x^{4}$ by $x^{- 5}$ by adding the exponents.

Move $x^{- 5}$ .

$8 (x^{- 5} x^{4}) y^{- 3} (\frac{1}{2} \cdot (y^{2}))$

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

$8 x^{- 5 + 4} y^{- 3} (\frac{1}{2} \cdot (y^{2}))$

Add $- 5$ and $4$ .

$8 x^{- 1} y^{- 3} (\frac{1}{2} \cdot (y^{2}))$

Step 2

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

Move $y^{2}$ .

$8 x^{- 1} (y^{2} y^{- 3}) \frac{1}{2}$

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

$8 x^{- 1} y^{2 - 3} \frac{1}{2}$

Subtract $3$ from $2$ .

$8 x^{- 1} y^{- 1} \frac{1}{2}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $8 x^{- 1} y^{- 1}$ .

$2 (4 x^{- 1} y^{- 1}) \frac{1}{2}$

Cancel the common factor.

$2 (4 x^{- 1} y^{- 1}) \frac{1}{2}$

Rewrite the expression.

$4 x^{- 1} y^{- 1}$

Step 4

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

$4 \frac{1}{x} y^{- 1}$

Step 5

Combine $4$ and $\frac{1}{x}$ .

$\frac{4}{x} y^{- 1}$

Step 6

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

$\frac{4}{x} \cdot \frac{1}{y}$

Step 7

Multiply $\frac{4}{x}$ by $\frac{1}{y}$ .

$\frac{4}{x y}$