Algebra Examples

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

Step 1

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

$\frac{1}{{(2 x^{2})}^{2}} \cdot {(2 x^{4})}^{2}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{1}{2^{2} {(x^{2})}^{2}} \cdot {(2 x^{4})}^{2}$

Step 2.2

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

$\frac{1}{4 {(x^{2})}^{2}} \cdot {(2 x^{4})}^{2}$

Step 2.3

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

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Step 2.3.1

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

$\frac{1}{4 x^{2 \cdot 2}} \cdot {(2 x^{4})}^{2}$

Step 2.3.2

Multiply $2$ by $2$ .

$\frac{1}{4 x^{4}} \cdot {(2 x^{4})}^{2}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Apply the product rule to $2 x^{4}$ .

$\frac{1}{4 x^{4}} \cdot (2^{2} {(x^{4})}^{2})$

Step 3.2

Simplify the expression.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2^{2} \frac{1}{4 x^{4}} {(x^{4})}^{2}$

Step 3.2.2

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

$4 \frac{1}{4 x^{4}} {(x^{4})}^{2}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $4 x^{4}$ .

$4 \frac{1}{4 (x^{4})} {(x^{4})}^{2}$

Step 3.3.2

Cancel the common factor.

$4 \frac{1}{4 x^{4}} {(x^{4})}^{2}$

Step 3.3.3

Rewrite the expression.

$\frac{1}{x^{4}} {(x^{4})}^{2}$

Step 3.4

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 3.4.1

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

$\frac{1}{x^{4}} x^{4 \cdot 2}$

Step 3.4.2

Multiply $4$ by $2$ .

$\frac{1}{x^{4}} x^{8}$

Step 3.5

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

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Step 3.5.1

Factor $x^{4}$ out of $x^{8}$ .

$\frac{1}{x^{4}} (x^{4} x^{4})$

Step 3.5.2

Cancel the common factor.

$\frac{1}{x^{4}} (x^{4} x^{4})$

Step 3.5.3

Rewrite the expression.

$x^{4}$