Algebra Examples

${(x^{- 2})}^{2} {(3 x y^{5})}^{4}$

Step 1

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

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Step 1.1

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

$x^{- 2 \cdot 2} {(3 x y^{5})}^{4}$

Step 1.2

Multiply $- 2$ by $2$ .

$x^{- 4} {(3 x y^{5})}^{4}$

Step 2

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

$\frac{1}{x^{4}} {(3 x y^{5})}^{4}$

Step 3

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

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Step 3.1

Apply the product rule to $3 x y^{5}$ .

$\frac{1}{x^{4}} ({(3 x)}^{4} {(y^{5})}^{4})$

Step 3.2

Apply the product rule to $3 x$ .

$\frac{1}{x^{4}} (3^{4} x^{4} {(y^{5})}^{4})$

Step 4

Simplify the expression.

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Step 4.1

Rewrite using the commutative property of multiplication.

$3^{4} \frac{1}{x^{4}} (x^{4} {(y^{5})}^{4})$

Step 4.2

Raise $3$ to the power of $4$ .

$81 \frac{1}{x^{4}} (x^{4} {(y^{5})}^{4})$

Step 5

Combine $81$ and $\frac{1}{x^{4}}$ .

$\frac{81}{x^{4}} (x^{4} {(y^{5})}^{4})$

Step 6

Cancel the common factor of $x^{4}$ .

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Step 6.1

Factor $x^{4}$ out of $x^{4} {(y^{5})}^{4}$ .

$\frac{81}{x^{4}} (x^{4} ({(y^{5})}^{4}))$

Step 6.2

Cancel the common factor.

$\frac{81}{x^{4}} (x^{4} {(y^{5})}^{4})$

Step 6.3

Rewrite the expression.

$81 {(y^{5})}^{4}$

Step 7

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

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Step 7.1

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

$81 y^{5 \cdot 4}$

Step 7.2

Multiply $5$ by $4$ .

$81 y^{20}$