Simplify (21x^5y^12)/((3x^-2y^7)^2)

$\frac{21 x^{5} y^{12}}{{(3 x^{- 2} y^{7})}^{2}}$

Step 1

Simplify the denominator.

Apply the product rule to $3 x^{- 2} y^{7}$ .

$\frac{21 x^{5} y^{12}}{{(3 x^{- 2})}^{2} {(y^{7})}^{2}}$

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

$\frac{21 x^{5} y^{12}}{{(3 \frac{1}{x^{2}})}^{2} {(y^{7})}^{2}}$

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

$\frac{21 x^{5} y^{12}}{{(\frac{3}{x^{2}})}^{2} {(y^{7})}^{2}}$

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

$\frac{21 x^{5} y^{12}}{\frac{3^{2}}{{(x^{2})}^{2}} {(y^{7})}^{2}}$

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

$\frac{21 x^{5} y^{12}}{\frac{9}{{(x^{2})}^{2}} {(y^{7})}^{2}}$

Multiply the exponents in ${(x^{2})}^{2}$ .

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

$\frac{21 x^{5} y^{12}}{\frac{9}{x^{2 \cdot 2}} {(y^{7})}^{2}}$

Multiply $2$ by $2$ .

$\frac{21 x^{5} y^{12}}{\frac{9}{x^{4}} {(y^{7})}^{2}}$

Multiply the exponents in ${(y^{7})}^{2}$ .

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

$\frac{21 x^{5} y^{12}}{\frac{9}{x^{4}} y^{7 \cdot 2}}$

Multiply $7$ by $2$ .

$\frac{21 x^{5} y^{12}}{\frac{9}{x^{4}} y^{14}}$

Step 2

Combine $\frac{9}{x^{4}}$ and $y^{14}$ .

$\frac{21 x^{5} y^{12}}{\frac{9 y^{14}}{x^{4}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$21 x^{5} y^{12} \frac{x^{4}}{9 y^{14}}$

Step 4

Cancel the common factor of $3 y^{12}$ .

Factor $3 y^{12}$ out of $21 x^{5} y^{12}$ .

$3 y^{12} (7 x^{5}) \frac{x^{4}}{9 y^{14}}$

Factor $3 y^{12}$ out of $9 y^{14}$ .

$3 y^{12} (7 x^{5}) \frac{x^{4}}{3 y^{12} (3 y^{2})}$

Cancel the common factor.

$3 y^{12} (7 x^{5}) \frac{x^{4}}{3 y^{12} (3 y^{2})}$

Rewrite the expression.

$7 x^{5} \frac{x^{4}}{3 y^{2}}$

Step 5

Combine $7$ and $\frac{x^{4}}{3 y^{2}}$ .

$x^{5} \frac{7 x^{4}}{3 y^{2}}$

Step 6

Combine $x^{5}$ and $\frac{7 x^{4}}{3 y^{2}}$ .

$\frac{x^{5} (7 x^{4})}{3 y^{2}}$

Step 7

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

Move $x^{4}$ .

$\frac{x^{4} x^{5} \cdot 7}{3 y^{2}}$

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

$\frac{x^{4 + 5} \cdot 7}{3 y^{2}}$

Add $4$ and $5$ .

$\frac{x^{9} \cdot 7}{3 y^{2}}$

Step 8

Move $7$ to the left of $x^{9}$ .

$\frac{7 x^{9}}{3 y^{2}}$

Simplify (21x^5y^12)/((3x^-2y^7)^2)

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