Evaluate. (-2(3)/(4))^(2)=

Identify Base and Exponent: Identify the base and the exponent. In the expression (-2(3)/(4))^2, -2(3)/(4) is the base raised to the exponent 2. Base: -2(3)/(4) Exponent: 2Simplify Base: Simplify the base before applying the exponent. The base -2(3)/(4) can be simplified by multiplying -2 by (3)/(4). Simplified Base: -2 * (3)/(4) = -6/4 = -3/2Apply Exponent: Apply the exponent to the simplified base. Now we raise the simplified base (-3/2) to the power of 2. (-3/2)^2 means (-3/2) is multiplied by itself. (-3/2)^2 = (-3/2) * (-3/2)Multiply Fractions: Multiply the fractions. To multiply fractions, multiply the numerators together and the denominators together. (-3/2) * (-3/2) = (9/4)Write Final Answer: Write the final answer. The simplest form of (-3/2)^2 is 9/4.

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Evaluate. $\newline$ $\left(-2 \frac{3}{4}\right)^{2}=$

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Math Problems

Grade 8

Powers with negative bases

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Q. Evaluate.

\newline

\left(-2 \frac{3}{4}\right)^{2}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $(-2(3)/(4))^2$ , $-2(3)/(4)$ is the base raised to the exponent $2$ . $\newline$ Base: $-2(3)/(4)$ $\newline$ Exponent: $2$
Simplify Base: Simplify the base before applying the exponent. $\newline$ The base $-2\left(\frac{3}{4}\right)$ can be simplified by multiplying $-2$ by $\left(\frac{3}{4}\right)$ . $\newline$ Simplified Base: $-2 \times \left(\frac{3}{4}\right) = -\frac{6}{4} = -\frac{3}{2}$
Apply Exponent: Apply the exponent to the simplified base. $\newline$ Now we raise the simplified base $(-\frac{3}{2})$ to the power of $2$ . $\newline$ $(-\frac{3}{2})^2$ means $(-\frac{3}{2})$ is multiplied by itself. $\newline$ $(-\frac{3}{2})^2 = (-\frac{3}{2}) \times (-\frac{3}{2})$
Multiply Fractions: Multiply the fractions. $\newline$ To multiply fractions, multiply the numerators together and the denominators together. $\newline$ $(-\frac{3}{2}) \times (-\frac{3}{2}) = \frac{9}{4}$
Write Final Answer: Write the final answer. $\newline$ The simplest form of $(-\frac{3}{2})^2$ is $\frac{9}{4}$ .