## Intermediate Algebra for College Students (7th Edition)

$$2^{-2} + \frac{1}{2}x^{0} =\frac{3}{4}$$
$$2^{-2} + \frac{1}{2}x^{0}$$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ and the zero exponent rule: $b^{0}=1$ Thus, $$2^{-2} + \frac{1}{2}x^{0}$$ can be simplified as $$\frac{1}{2^{2}} + \frac{1}{2}$$ $$\frac{1}{4} + \frac{1}{2}$$ Find the least common multiple (LCM) of the factors $4$ and $2$: $4: 2 \times 2$ $2: 2$ Adjust the fractions using the LCM: $$\frac{1}{4} + \frac{1}{2}$$ $$=\frac{1}{4} + \frac{2}{4}$$ $$=\frac{3}{4}$$