Questions: Simplify: (1 / 2w^2)^(-2).

Solution Steps

To simplify the expression \(\left(\frac{1}{2 w^{2}}\right)^{-2}\), we can use the property of exponents that states \((a/b)^{-n} = (b/a)^{n}\). This means we can flip the fraction and change the sign of the exponent to positive. Then, we apply the positive exponent to both the numerator and the denominator.

We start with the expression

\[ \left(\frac{1}{2 w^{2}}\right)^{-2} \]

Using the property of exponents, we can rewrite this as

\[ \left(\frac{2 w^{2}}{1}\right)^{2} = (2 w^{2})^{2} \]

Next, we expand the expression

\[ (2 w^{2})^{2} \]

This can be calculated as

\[ 2^{2} \cdot (w^{2})^{2} = 4 \cdot w^{4} \]

Thus, the simplified form of the original expression is

\[ 4 w^{4} \]

Final Answer