Simplify (40x^3y^9)/((2x^6y^-10)^-3)

$\frac{40 x^{3} y^{9}}{{(2 x^{6} y^{- 10})}^{- 3}}$

Step 1

Move ${(2 x^{6} y^{- 10})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$40 x^{3} y^{9} {(2 x^{6} y^{- 10})}^{3}$

Step 2

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

$40 x^{3} y^{9} {(2 x^{6} \frac{1}{y^{10}})}^{3}$

Step 3

Multiply $2 x^{6} \frac{1}{y^{10}}$ .

Combine $2$ and $\frac{1}{y^{10}}$ .

$40 x^{3} y^{9} {(x^{6} \frac{2}{y^{10}})}^{3}$

Combine $x^{6}$ and $\frac{2}{y^{10}}$ .

$40 x^{3} y^{9} {(\frac{x^{6} \cdot 2}{y^{10}})}^{3}$

Step 4

Move $2$ to the left of $x^{6}$ .

$40 x^{3} y^{9} {(\frac{2 \cdot x^{6}}{y^{10}})}^{3}$

Step 5

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

Apply the product rule to $\frac{2 x^{6}}{y^{10}}$ .

$40 x^{3} y^{9} \frac{{(2 x^{6})}^{3}}{{(y^{10})}^{3}}$

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

$40 x^{3} y^{9} \frac{2^{3} {(x^{6})}^{3}}{{(y^{10})}^{3}}$

Step 6

Simplify the numerator.

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

$40 x^{3} y^{9} \frac{8 {(x^{6})}^{3}}{{(y^{10})}^{3}}$

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

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

$40 x^{3} y^{9} \frac{8 x^{6 \cdot 3}}{{(y^{10})}^{3}}$

Multiply $6$ by $3$ .

$40 x^{3} y^{9} \frac{8 x^{18}}{{(y^{10})}^{3}}$

Step 7

Simplify terms.

Multiply the exponents in ${(y^{10})}^{3}$ .

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

$40 x^{3} y^{9} \frac{8 x^{18}}{y^{10 \cdot 3}}$

Multiply $10$ by $3$ .

$40 x^{3} y^{9} \frac{8 x^{18}}{y^{30}}$

Cancel the common factor of $y^{9}$ .

Factor $y^{9}$ out of $40 x^{3} y^{9}$ .

$y^{9} (40 x^{3}) \frac{8 x^{18}}{y^{30}}$

Factor $y^{9}$ out of $y^{30}$ .

$y^{9} (40 x^{3}) \frac{8 x^{18}}{y^{9} y^{21}}$

Cancel the common factor.

$y^{9} (40 x^{3}) \frac{8 x^{18}}{y^{9} y^{21}}$

Rewrite the expression.

$40 x^{3} \frac{8 x^{18}}{y^{21}}$

Combine $40$ and $\frac{8 x^{18}}{y^{21}}$ .

$x^{3} \frac{40 (8 x^{18})}{y^{21}}$

Multiply $8$ by $40$ .

$x^{3} \frac{320 x^{18}}{y^{21}}$

Combine $x^{3}$ and $\frac{320 x^{18}}{y^{21}}$ .

$\frac{x^{3} (320 x^{18})}{y^{21}}$

Step 8

Multiply $x^{3}$ by $x^{18}$ by adding the exponents.

Move $x^{18}$ .

$\frac{x^{18} x^{3} \cdot 320}{y^{21}}$

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

$\frac{x^{18 + 3} \cdot 320}{y^{21}}$

Add $18$ and $3$ .

$\frac{x^{21} \cdot 320}{y^{21}}$

Step 9

Move $320$ to the left of $x^{21}$ .

$\frac{320 x^{21}}{y^{21}}$

Simplify (40x^3y^9)/((2x^6y^-10)^-3)

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