Algebra Examples

$\frac{{(6 x^{- 2} y^{2})}^{- 1}}{{(6^{4} x^{4} y^{5})}^{- 4}}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{1}{{(6^{4} x^{4} y^{5})}^{- 4} (6 x^{- 2} y^{2})}$

Step 1.2

Move ${(6^{4} x^{4} y^{5})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(6^{4} x^{4} y^{5})}^{4}}{6 x^{- 2} y^{2}}$

Step 1.3

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(6^{4} x^{4} y^{5})}^{4} x^{2}}{6 y^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $6^{4} x^{4} y^{5}$ .

$\frac{{(6^{4} x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Step 2.2

Raise $6$ to the power of $4$ .

$\frac{{(1296 x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Step 2.3

Apply the product rule to $1296 x^{4}$ .

$\frac{1296^{4} {(x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Step 2.4

Raise $1296$ to the power of $4$ .

$\frac{2821109907456 {(x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{2821109907456 x^{4 \cdot 4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Step 2.5.2

Multiply $4$ by $4$ .

$\frac{2821109907456 x^{16} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Step 2.6

Multiply the exponents in ${(y^{5})}^{4}$ .

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Step 2.6.1

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

$\frac{2821109907456 x^{16} y^{5 \cdot 4} x^{2}}{6 y^{2}}$

Step 2.6.2

Multiply $5$ by $4$ .

$\frac{2821109907456 x^{16} y^{20} x^{2}}{6 y^{2}}$

Step 2.7

Multiply $x^{16}$ by $x^{2}$ by adding the exponents.

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Step 2.7.1

Move $x^{2}$ .

$\frac{2821109907456 (x^{2} x^{16}) y^{20}}{6 y^{2}}$

Step 2.7.2

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

$\frac{2821109907456 x^{2 + 16} y^{20}}{6 y^{2}}$

Step 2.7.3

Add $2$ and $16$ .

$\frac{2821109907456 x^{18} y^{20}}{6 y^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $2821109907456$ and $6$ .

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Step 3.1.1

Factor $6$ out of $2821109907456 x^{18} y^{20}$ .

$\frac{6 (470184984576 x^{18} y^{20})}{6 y^{2}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $6$ out of $6 y^{2}$ .

$\frac{6 (470184984576 x^{18} y^{20})}{6 (y^{2})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{6 (470184984576 x^{18} y^{20})}{6 y^{2}}$

Step 3.1.2.3

Rewrite the expression.

$\frac{470184984576 x^{18} y^{20}}{y^{2}}$

Step 3.2

Cancel the common factor of $y^{20}$ and $y^{2}$ .

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Step 3.2.1

Factor $y^{2}$ out of $470184984576 x^{18} y^{20}$ .

$\frac{y^{2} (470184984576 x^{18} y^{18})}{y^{2}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Multiply by $1$ .

$\frac{y^{2} (470184984576 x^{18} y^{18})}{y^{2} \cdot 1}$

Step 3.2.2.2

Cancel the common factor.

$\frac{y^{2} (470184984576 x^{18} y^{18})}{y^{2} \cdot 1}$

Step 3.2.2.3

Rewrite the expression.

$\frac{470184984576 x^{18} y^{18}}{1}$

Step 3.2.2.4

Divide $470184984576 x^{18} y^{18}$ by $1$ .

$470184984576 x^{18} y^{18}$