Solve (1/4)² + 1/16: Computing Squares and Sums of Fractions

Let's solve the problem step-by-step using the order of operations, specifically addressing powers and fractions.

Given the expression: $(\frac{1}{4})^2+\frac{1}{16}$

• First, evaluate the power: $(\frac{1}{4})^2$
• Squaring a fraction means squaring both the numerator and the denominator:
• $(\frac{1}{4})^2 = \frac{1^2}{4^2} = \frac{1}{16}$
• Next, add the fractions: $\frac{1}{16} + \frac{1}{16}$
• Since the denominators are the same, simply add the numerators:
• $\frac{1+1}{16} = \frac{2}{16} = \frac{1}{8}$

Therefore, the value of the expression is $\frac{1}{8}$.