Evaluate. (-(1)/(2))^(5)=

Identify Base and Exponent: Identify the base and the exponent. In the expression (-(1/2))^5, -(1/2) is the base raised to the exponent 5. Base: -(1/2) Exponent: 5Choose Expanded Form: Choose the expanded form of (-(1/2))^5. The base is -(1/2) and the exponent is 5. So, (-(1/2))^5 means -(1/2) is multiplied by itself 5 times. Expanded Form of (-(1/2))^5: (-(1/2)) × (-(1/2)) × (-(1/2)) × (-(1/2)) × (-(1/2))Multiply and Simplify: (-(1/2))^5 = (-(1/2)) × (-(1/2)) × (-(1/2)) × (-(1/2)) × (-(1/2)) Multiply to write in simplest form. When multiplying negative numbers an odd number of times, the result is negative. (-(1/2))^5 = (-(1/2)) × (-(1/2)) × (-(1/2)) × (-(1/2)) × (-(1/2)) = -1/32 The simplest form of (-(1/2))^5 is -1/32.

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Evaluate. $\newline$ $\left(-\frac{1}{2}\right)^{5}=$

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Math Problems

Grade 8

Powers with negative bases

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Q. Evaluate.

\newline

\left(-\frac{1}{2}\right)^{5}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $\left(-\frac{1}{2}\right)^5$ , $-\frac{1}{2}$ is the base raised to the exponent $5$ . $\newline$ Base: $-\frac{1}{2}$ $\newline$ Exponent: $5$
Choose Expanded Form: Choose the expanded form of $\left(-\frac{1}{2}\right)^5$ . The base is $-\frac{1}{2}$ and the exponent is $5$ . So, $\left(-\frac{1}{2}\right)^5$ means $-\frac{1}{2}$ is multiplied by itself $5$ times. Expanded Form of $\left(-\frac{1}{2}\right)^5$ : $\left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right)$
Multiply and Simplify: $(-(1/2))^5 = (-(1/2)) \times (-(1/2)) \times (-(1/2)) \times (-(1/2)) \times (-(1/2))$ $\newline$ Multiply to write in simplest form. $\newline$ When multiplying negative numbers an odd number of times, the result is negative. $\newline$ $(-(1/2))^5$ $\newline$ $= (-(1/2)) \times (-(1/2)) \times (-(1/2)) \times (-(1/2)) \times (-(1/2))$ $\newline$ $= -1/32$ $\newline$ The simplest form of $(-(1/2))^5$ is $-1/32$ .