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

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

Step 1

Simplify the numerator.

Apply the product rule to $2 x^{- 3} y^{4}$ .

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

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

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

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

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

Apply the product rule to $\frac{2}{x^{3}}$ .

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

Raise $2$ to the power of $3$ .

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

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

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

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

Multiply $3$ by $3$ .

$\frac{\frac{8}{x^{9}} {(y^{4})}^{3}}{{(4 x y)}^{2}}$

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

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

$\frac{\frac{8}{x^{9}} y^{4 \cdot 3}}{{(4 x y)}^{2}}$

Multiply $4$ by $3$ .

$\frac{\frac{8}{x^{9}} y^{12}}{{(4 x y)}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $4 x y$ .

$\frac{\frac{8}{x^{9}} y^{12}}{{(4 x)}^{2} y^{2}}$

Apply the product rule to $4 x$ .

$\frac{\frac{8}{x^{9}} y^{12}}{4^{2} x^{2} y^{2}}$

Raise $4$ to the power of $2$ .

$\frac{\frac{8}{x^{9}} y^{12}}{16 x^{2} y^{2}}$

Step 3

Combine $\frac{8}{x^{9}}$ and $y^{12}$ .

$\frac{\frac{8 y^{12}}{x^{9}}}{16 x^{2} y^{2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 y^{12}}{x^{9}} \cdot \frac{1}{16 x^{2} y^{2}}$

Step 5

Combine.

$\frac{8 y^{12} \cdot 1}{x^{9} (16 x^{2} y^{2})}$

Step 6

Multiply $x^{9}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{8 y^{12} \cdot 1}{x^{2} x^{9} (16 y^{2})}$

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

$\frac{8 y^{12} \cdot 1}{x^{2 + 9} (16 y^{2})}$

Add $2$ and $9$ .

$\frac{8 y^{12} \cdot 1}{x^{11} (16 y^{2})}$

Step 7

Multiply $8 y^{12}$ by $1$ .

$\frac{8 y^{12}}{x^{11} (16 y^{2})}$

Step 8

Cancel the common factor of $8$ and $16$ .

Factor $8$ out of $8 y^{12}$ .

$\frac{8 (y^{12})}{x^{11} (16 y^{2})}$

Cancel the common factors.

Factor $8$ out of $x^{11} (16 y^{2})$ .

$\frac{8 (y^{12})}{8 (x^{11} (2 y^{2}))}$

Cancel the common factor.

$\frac{8 y^{12}}{8 (x^{11} (2 y^{2}))}$

Rewrite the expression.

$\frac{y^{12}}{x^{11} (2 y^{2})}$

Step 9

Cancel the common factor of $y^{12}$ and $y^{2}$ .

Factor $y^{2}$ out of $y^{12}$ .

$\frac{y^{2} y^{10}}{x^{11} (2 y^{2})}$

Cancel the common factors.

Factor $y^{2}$ out of $x^{11} (2 y^{2})$ .

$\frac{y^{2} y^{10}}{y^{2} (x^{11} \cdot (2))}$

Cancel the common factor.

$\frac{y^{2} y^{10}}{y^{2} (x^{11} \cdot (2))}$

Rewrite the expression.

$\frac{y^{10}}{x^{11} \cdot (2)}$

Step 10

Move $2$ to the left of $x^{11}$ .

$\frac{y^{10}}{2 x^{11}}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.