Evaluate. (-4(1)/(2))^(2)=

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

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Math Problems

Grade 8

Powers with negative bases

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{ $49$ }{ $4$ }.