Simplify (8x^7y^2)(2x^-1y^-6)^3

$(8 x^{7} y^{2}) {(2 x^{- 1} y^{- 6})}^{3}$

Step 1

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

$8 x^{7} y^{2} {(2 \frac{1}{x} y^{- 6})}^{3}$

Step 2

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

$8 x^{7} y^{2} {(\frac{2}{x} y^{- 6})}^{3}$

Step 3

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

$8 x^{7} y^{2} {(\frac{2}{x} \cdot \frac{1}{y^{6}})}^{3}$

Step 4

Combine.

$8 x^{7} y^{2} {(\frac{2 \cdot 1}{x y^{6}})}^{3}$

Step 5

Multiply $2$ by $1$ .

$8 x^{7} y^{2} {(\frac{2}{x y^{6}})}^{3}$

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2}{x y^{6}}$ .

$8 x^{7} y^{2} \frac{2^{3}}{{(x y^{6})}^{3}}$

Apply the product rule to $x y^{6}$ .

$8 x^{7} y^{2} \frac{2^{3}}{x^{3} {(y^{6})}^{3}}$

Step 7

Simplify the expression.

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

$8 x^{7} y^{2} \frac{8}{x^{3} {(y^{6})}^{3}}$

Multiply the exponents in ${(y^{6})}^{3}$ .

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

$8 x^{7} y^{2} \frac{8}{x^{3} y^{6 \cdot 3}}$

Multiply $6$ by $3$ .

$8 x^{7} y^{2} \frac{8}{x^{3} y^{18}}$

Step 8

Cancel the common factor of $x^{3} y^{2}$ .

Factor $x^{3} y^{2}$ out of $8 x^{7} y^{2}$ .

$x^{3} y^{2} (8 x^{4}) \frac{8}{x^{3} y^{18}}$

Factor $x^{3} y^{2}$ out of $x^{3} y^{18}$ .

$x^{3} y^{2} (8 x^{4}) \frac{8}{x^{3} y^{2} (y^{16})}$

Cancel the common factor.

$x^{3} y^{2} (8 x^{4}) \frac{8}{x^{3} y^{2} y^{16}}$

Rewrite the expression.

$8 x^{4} \frac{8}{y^{16}}$

Step 9

Combine $8$ and $\frac{8}{y^{16}}$ .

$x^{4} \frac{8 \cdot 8}{y^{16}}$

Step 10

Multiply $8$ by $8$ .

$x^{4} \frac{64}{y^{16}}$

Step 11

Combine $x^{4}$ and $\frac{64}{y^{16}}$ .

$\frac{x^{4} \cdot 64}{y^{16}}$

Step 12

Move $64$ to the left of $x^{4}$ .

$\frac{64 x^{4}}{y^{16}}$

Simplify (8x^7y^2)(2x^-1y^-6)^3

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