Algebra Examples

$x \cdot 2^{3} \cdot {(\frac{4}{x^{2}})}^{- 1}$

Step 1

Raise $2$ to the power of $3$ .

$x \cdot 8 \cdot {(\frac{4}{x^{2}})}^{- 1}$

Step 2

Move $8$ to the left of $x$ .

$8 \cdot x \cdot {(\frac{4}{x^{2}})}^{- 1}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$8 x \cdot \frac{x^{2}}{4}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Factor $4$ out of $8 x$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$2 x \cdot x^{2}$

Step 5

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

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Step 5.1

Move $x^{2}$ .

$2 (x^{2} x)$

Step 5.2

Multiply $x^{2}$ by $x$ .

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Step 5.2.1

Raise $x$ to the power of $1$ .

$2 (x^{2} x^{1})$

Step 5.2.2

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

$2 x^{2 + 1}$

Step 5.3

Add $2$ and $1$ .

$2 x^{3}$