Evaluate. $\newline$ $\left(-4 \frac{1}{2}\right)^{2}=$

Full solution

Q. Evaluate.

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\left(-4 \frac{1}{2}\right)^{2}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $(-4(1)/(2))^2$ , $-4(1)/(2)$ is the base raised to the exponent $2$ . $\newline$ Base: $-4(1)/(2)$ $\newline$ Exponent: $2$
Rewrite Base as Fraction: Rewrite the base as a single fraction. $\newline$ The base $-4\left(\frac{1}{2}\right)$ can be rewritten as $-4 + \frac{1}{2}$ which simplifies to $-\frac{8}{2} + \frac{1}{2}$ , which is $-\frac{7}{2}$ . $\newline$ So, $(-4\left(\frac{1}{2}\right))^2$ becomes $(-\frac{7}{2})^2$ .
Choose Expanded Form: Choose the expanded form of $(-\frac{7}{2})^2$ . The base is $-\frac{7}{2}$ and the exponent is $2$ . So, $(-\frac{7}{2})^2$ means $-\frac{7}{2}$ is multiplied by itself once. Expanded Form of $(-\frac{7}{2})^2$ : $(-\frac{7}{2}) \times (-\frac{7}{2})$
Multiply for Simplest Form: Multiply to write in simplest form. $\newline$ $(-\frac{7}{2})^2$ $\newline$ = $(-\frac{7}{2}) \times (-\frac{7}{2})$ $\newline$ = \frac{ $49$ }{ $4$ } $\newline$ The simplest form of $(-\frac{7}{2})^2$ is \frac{ $49$ }{ $4$ }.