Evaluate (6x^-2)^2(0.5x)^4

${(6 x^{- 2})}^{2} {(0.5 x)}^{4}$

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

${(6 \frac{1}{x^{2}})}^{2} {(0.5 x)}^{4}$

Combine $6$ and $\frac{1}{x^{2}}$ .

${(\frac{6}{x^{2}})}^{2} {(0.5 x)}^{4}$

Simplify the expression.

Apply the product rule to $\frac{6}{x^{2}}$ .

$\frac{6^{2}}{{(x^{2})}^{2}} {(0.5 x)}^{4}$

Raise $6$ to the power of $2$ .

$\frac{36}{{(x^{2})}^{2}} {(0.5 x)}^{4}$

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

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

$\frac{36}{x^{2 \cdot 2}} {(0.5 x)}^{4}$

Multiply $2$ by $2$ .

$\frac{36}{x^{4}} {(0.5 x)}^{4}$

Apply the product rule to $0.5 x$ .

$\frac{36}{x^{4}} ({0.5}^{4} x^{4})$

Rewrite using the commutative property of multiplication.

${0.5}^{4} \frac{36}{x^{4}} x^{4}$

Raise $0.5$ to the power of $4$ .

$0.0625 \frac{36}{x^{4}} x^{4}$

Multiply $0.0625 \frac{36}{x^{4}}$ .

Combine $0.0625$ and $\frac{36}{x^{4}}$ .

$\frac{0.0625 \cdot 36}{x^{4}} x^{4}$

Multiply $0.0625$ by $36$ .

$\frac{2.25}{x^{4}} x^{4}$

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

Cancel the common factor.

$\frac{2.25}{x^{4}} x^{4}$

Rewrite the expression.

$2.25$