Evaluate 4x^-4*1/2x^2

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

Step 1

Multiply $x^{- 4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Subtract $4$ from $2$ .

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

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $4 x^{- 2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x^{- 2}$

Step 3

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

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

Step 4

Combine $2$ and $\frac{1}{x^{2}}$ .

$\frac{2}{x^{2}}$