Algebra Examples

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

Step 1

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

$64 \cdot x^{2} \cdot {(\frac{4}{x})}^{- 2}$

Step 2

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

$64 x^{2} \cdot {(\frac{x}{4})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{x}{4}$ .

$64 x^{2} \cdot \frac{x^{2}}{4^{2}}$

Step 3.2

Raise $4$ to the power of $2$ .

$64 x^{2} \cdot \frac{x^{2}}{16}$

Step 4

Cancel the common factor of $16$ .

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Step 4.1

Factor $16$ out of $64 x^{2}$ .

$16 (4 x^{2}) \cdot \frac{x^{2}}{16}$

Step 4.2

Cancel the common factor.

$16 (4 x^{2}) \cdot \frac{x^{2}}{16}$

Step 4.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

Move $x^{2}$ .

$4 (x^{2} x^{2})$

Step 5.2

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

$4 x^{2 + 2}$

Step 5.3

Add $2$ and $2$ .

$4 x^{4}$