Evaluate. ((1)/(2))^(3)=

Identify base and exponent: Identify the base and the exponent. In the expression ((1)/(2))^(3), (1/2) is the base raised to the exponent 3. Base: 1/2 Exponent: 3Choose expanded form: Choose the expanded form of ((1)/(2))^(3). The base is 1/2 and the exponent is 3. So, ((1)/(2))^(3) means (1/2) is multiplied by itself 3 times. Expanded Form of ((1)/(2))^(3): (1/2) × (1/2) × (1/2)Multiply to simplify: ((1)/(2))^(3) = (1/2) × (1/2) × (1/2) Multiply to write in simplest form. ((1)/(2))^(3) = (1/2) × (1/2) × (1/2) = (1×1×1)/(2×2×2) = 1/8 The simplest form of ((1)/(2))^(3) is 1/8.

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Math Problems

Grade 8

Powers with negative bases

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Q. Evaluate.

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(\frac{1}{2})^{3}=

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $(\frac{1}{2})^{3}$ , $(\frac{1}{2})$ is the base raised to the exponent $3$ . $\newline$ Base: $\frac{1}{2}$ $\newline$ Exponent: $3$
Choose expanded form: Choose the expanded form of $((1)/(2))^3$ . $\newline$ The base is $1/2$ and the exponent is $3$ . $\newline$ So, $((1)/(2))^3$ means $(1/2)$ is multiplied by itself $3$ times. $\newline$ Expanded Form of $((1)/(2))^3$ : $\newline$ $(1/2) \times (1/2) \times (1/2)$
Multiply to simplify: $\left(\frac{1}{2}\right)^3 = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)$ $\newline$ Multiply to write in simplest form. $\newline$ $\left(\frac{1}{2}\right)^3$ $\newline$ $= \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)$ $\newline$ $= \frac{1\times1\times1}{2\times2\times2}$ $\newline$ $= \frac{1}{8}$ $\newline$ The simplest form of $\left(\frac{1}{2}\right)^3$ is $\frac{1}{8}$ .