Chapter 1, Problem 6SAP

To determine

To select: the value of ${\left(-4\right)}^2+{\left(2\right)}^{-4}+\frac{3}{4}$ from the given options.

Answer to Problem 6SAP

A. $16\frac{13}{16}$

Explanation of Solution

Given information:

The given problem is ${\left(-4\right)}^2+{\left(2\right)}^{-4}+\frac{3}{4}$

The given options are as follows:

1. $16\frac{13}{16}$
2. $16\frac{3}{4}$
3. $-15\frac{7}{32}$
4. $15\frac{7}{32}$
5. 16

Calculation:

The given problem can be simplified as follows:

  $\begin{array}{c}{\left(-4\right)}^2+{\left(2\right)}^{-4}+\frac{3}{4}={\left(-4\right)}^2+\frac{1}{{\left(2\right)}^4}+\frac{3}{4}\left[\text{Rearranging the exponents}\right]\\ =16+\frac{1}{16}+\frac{3}{4}\left[\text{Solving the exponents}\right]\\ =16\left(\frac{16}{16}\right)+\frac{1}{16}+\frac{3}{4}\left(\frac{4}{4}\right)\left[\text{Taking common denominator}\right]\\ =\frac{256}{16}+\frac{1}{16}+\frac{12}{16}\\ =\frac{269}{16}\\ =16\frac{13}{16}\left[\text{Converting into mixed fraction}\right]\end{array}$

Thus, option A is correct.