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$(\frac{1}{2})^{-2} + 3^{0}$

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Understanding negative exponents

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Q.

(\frac{1}{2})^{-2} + 3^{0}

Evaluate Exponent: Evaluate the first term $(\frac{1}{2})^{-2}$ by finding the reciprocal of $(\frac{1}{2})^2$ . A negative exponent means that we take the reciprocal of the base raised to the positive of that exponent. $(\frac{1}{2})^{-2} = (\frac{2}{1})^2$
Calculate Fraction Square: Calculate the square of $\frac{2}{1}$ . $\newline$ When we square a fraction, we square both the numerator and the denominator. $\newline$ $(\frac{2}{1})^2 = 2^2 / 1^2 = \frac{4}{1} = 4$
Evaluate Zero Exponent: Evaluate the second term $3^0$ . Any non-zero number raised to the power of $0$ is $1$ . $3^0 = 1$
Add Calculated Values: Add the results from Step $2$ and Step $3$ . $\newline$ Now we add the two values we have calculated. $\newline$ $4 + 1 = 5$

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