Question

SIMPLIFYING EXPRESSIONS Simplify the expression. $$ \frac{1}{(2 x)^{-2}} $$

Short answer

The simplified form of the expression is \(4x^2\)

Step-by-step solution

Identify the expression

The expression to be simplified is \( \frac{1}{(2x)^{-2}} \)

Use the exponent rule

The rule \(a^{-n} = \frac{1}{a^n}\) can be used to simplify this expression. Apply this to the given expression, \( (2x)^{-2} \) becomes \( \frac{1}{(2x)^2} \). So, the expression becomes \( \frac{1}{\frac{1}{(2x)^2}} \)

Simplify the fraction

This is a fraction of fractions. Simplify by multiplying the numerator and the denominator of the outer fraction by \((2x)^2\). This will remove the denominator. So, the expression simplifies to \((2x)^2\)

Expand the expression

The expression \((2x)^2\) can be expanded to \(4x^2\) so this is the simplest form of the expression