Pre-Algebra Examples

${(2 b^{- 2})}^{- 2}$

Step 1

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

${(2 \frac{1}{b^{2}})}^{- 2}$

Step 2

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

${(\frac{2}{b^{2}})}^{- 2}$

Step 3

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

${(\frac{b^{2}}{2})}^{2}$

Step 4

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

$\frac{{(b^{2})}^{2}}{2^{2}}$

Step 5

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

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Step 5.1

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

$\frac{b^{2 \cdot 2}}{2^{2}}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{b^{4}}{2^{2}}$

Step 6

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

$\frac{b^{4}}{4}$