Algebra Examples

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

Step 1

Multiply $x^{- 4}$ by $x^{6}$ by adding the exponents.

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Step 1.1

Move $x^{6}$ .

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

Step 1.2

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

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

Step 1.3

Subtract $4$ from $6$ .

${(\frac{x^{2}}{x^{2} \cdot 2})}^{5}$

Step 2

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

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Step 2.1

Cancel the common factor.

${(\frac{x^{2}}{x^{2} \cdot 2})}^{5}$

Step 2.2

Rewrite the expression.

${(\frac{1}{2})}^{5}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{5}}{2^{5}}$

Step 3.2

One to any power is one.

$\frac{1}{2^{5}}$

Step 3.3

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

$\frac{1}{32}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{32}$

Decimal Form:

$0.03125$