Algebra Examples

$\frac{{(2 x^{- 3} y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

$\frac{{(2 x^{- 3})}^{5} {(y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.2

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

$\frac{{(2 \frac{1}{x^{3}})}^{5} {(y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.3

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

$\frac{{(\frac{2}{x^{3}})}^{5} {(y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.4

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

$\frac{\frac{2^{5}}{{(x^{3})}^{5}} {(y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.5

Raise $2$ to the power of $5$ .

$\frac{\frac{32}{{(x^{3})}^{5}} {(y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.6

Multiply the exponents in ${(x^{3})}^{5}$ .

Tap for more steps...

Step 1.6.1

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

$\frac{\frac{32}{x^{3 \cdot 5}} {(y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.6.2

Multiply $3$ by $5$ .

$\frac{\frac{32}{x^{15}} {(y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.7

Multiply the exponents in ${(y^{- 2})}^{5}$ .

Tap for more steps...

Step 1.7.1

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

$\frac{\frac{32}{x^{15}} y^{- 2 \cdot 5}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.7.2

Multiply $- 2$ by $5$ .

$\frac{\frac{32}{x^{15}} y^{- 10}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 1.8

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

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{{(6 x^{- 1} y^{- 8})}^{2}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $6 x^{- 1} y^{- 8}$ .

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{{(6 x^{- 1})}^{2} {(y^{- 8})}^{2}}$

Step 2.2

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

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{{(6 \frac{1}{x})}^{2} {(y^{- 8})}^{2}}$

Step 2.3

Combine $6$ and $\frac{1}{x}$ .

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{{(\frac{6}{x})}^{2} {(y^{- 8})}^{2}}$

Step 2.4

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

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{\frac{6^{2}}{x^{2}} {(y^{- 8})}^{2}}$

Step 2.5

Raise $6$ to the power of $2$ .

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{\frac{36}{x^{2}} {(y^{- 8})}^{2}}$

Step 2.6

Multiply the exponents in ${(y^{- 8})}^{2}$ .

Tap for more steps...

Step 2.6.1

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

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{\frac{36}{x^{2}} y^{- 8 \cdot 2}}$

Step 2.6.2

Multiply $- 8$ by $2$ .

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{\frac{36}{x^{2}} y^{- 16}}$

Step 2.7

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

$\frac{\frac{32}{x^{15}} \cdot \frac{1}{y^{10}}}{\frac{36}{x^{2}} \cdot \frac{1}{y^{16}}}$

Step 3

Combine fractions.

Tap for more steps...

Step 3.1

Multiply $\frac{32}{x^{15}}$ by $\frac{1}{y^{10}}$ .

$\frac{\frac{32}{x^{15} y^{10}}}{\frac{36}{x^{2}} \cdot \frac{1}{y^{16}}}$

Step 3.2

Multiply $\frac{36}{x^{2}}$ by $\frac{1}{y^{16}}$ .

$\frac{\frac{32}{x^{15} y^{10}}}{\frac{36}{x^{2} y^{16}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{32}{x^{15} y^{10}} \cdot \frac{x^{2} y^{16}}{36}$

Step 5

Combine.

$\frac{32 (x^{2} y^{16})}{x^{15} y^{10} \cdot 36}$

Step 6

Cancel the common factor of $32$ and $36$ .

Tap for more steps...

Step 6.1

Factor $4$ out of $32 (x^{2} y^{16})$ .

$\frac{4 (8 (x^{2} y^{16}))}{x^{15} y^{10} \cdot 36}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $4$ out of $x^{15} y^{10} \cdot 36$ .

$\frac{4 (8 (x^{2} y^{16}))}{4 (x^{15} y^{10} \cdot 9)}$

Step 6.2.2

Cancel the common factor.

$\frac{4 (8 (x^{2} y^{16}))}{4 (x^{15} y^{10} \cdot 9)}$

Step 6.2.3

Rewrite the expression.

$\frac{8 (x^{2} y^{16})}{x^{15} y^{10} \cdot 9}$

Step 7

Cancel the common factor of $x^{2}$ and $x^{15}$ .

Tap for more steps...

Step 7.1

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

$\frac{x^{2} (8 (y^{16}))}{x^{15} y^{10} \cdot 9}$

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $x^{2}$ out of $x^{15} y^{10} \cdot 9$ .

$\frac{x^{2} (8 (y^{16}))}{x^{2} (x^{13} y^{10} \cdot 9)}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{2} (8 (y^{16}))}{x^{2} (x^{13} y^{10} \cdot 9)}$

Step 7.2.3

Rewrite the expression.

$\frac{8 (y^{16})}{x^{13} y^{10} \cdot 9}$

Step 8

Cancel the common factor of $y^{16}$ and $y^{10}$ .

Tap for more steps...

Step 8.1

Factor $y^{10}$ out of $8 (y^{16})$ .

$\frac{y^{10} (8 (y^{6}))}{x^{13} y^{10} \cdot 9}$

Step 8.2

Cancel the common factors.

Tap for more steps...

Step 8.2.1

Factor $y^{10}$ out of $x^{13} y^{10} \cdot 9$ .

$\frac{y^{10} (8 (y^{6}))}{y^{10} (x^{13} \cdot 9)}$

Step 8.2.2

Cancel the common factor.

$\frac{y^{10} (8 (y^{6}))}{y^{10} (x^{13} \cdot 9)}$

Step 8.2.3

Rewrite the expression.

$\frac{8 (y^{6})}{x^{13} \cdot 9}$

Step 9

Move $9$ to the left of $x^{13}$ .

$\frac{8 y^{6}}{9 x^{13}}$