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

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

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

Move $x$ .

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

Multiply $x$ by $x^{- 2}$ .

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

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

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

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

Subtract $2$ from $1$ .

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

Multiply $y^{3}$ by $y^{- 8}$ by adding the exponents.

Move $y^{- 8}$ .

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

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

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

Add $- 8$ and $3$ .

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

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move $y^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Multiply $y^{- 2}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

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

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

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

Subtract $2$ from $5$ .

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

Multiply $3$ by $5$ .

$\frac{15}{{(x^{- 3})}^{4} y^{3} x}$

Simplify the denominator.

Multiply the exponents in ${(x^{- 3})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{15}{x^{- 3 \cdot 4} y^{3} x}$

Multiply $- 3$ by $4$ .

$\frac{15}{x^{- 12} y^{3} x}$

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

$\frac{15}{\frac{1}{x^{12}} y^{3} x}$

Combine exponents.

Combine $\frac{1}{x^{12}}$ and $y^{3}$ .

$\frac{15}{\frac{y^{3}}{x^{12}} x}$

Combine $\frac{y^{3}}{x^{12}}$ and $x$ .

$\frac{15}{\frac{y^{3} x}{x^{12}}}$

Reduce the expression $\frac{y^{3} x}{x^{12}}$ by cancelling the common factors.

Factor $x$ out of $y^{3} x$ .

$\frac{15}{\frac{x y^{3}}{x^{12}}}$

Factor $x$ out of $x^{12}$ .

$\frac{15}{\frac{x y^{3}}{x \cdot x^{11}}}$

Cancel the common factor.

$\frac{15}{\frac{x y^{3}}{x \cdot x^{11}}}$

Rewrite the expression.

$\frac{15}{\frac{y^{3}}{x^{11}}}$

Multiply the numerator by the reciprocal of the denominator.

$15 \frac{x^{11}}{y^{3}}$

Combine $15$ and $\frac{x^{11}}{y^{3}}$ .

$\frac{15 x^{11}}{y^{3}}$

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

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