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

Identify base and exponent: Identify the base and the exponent. In the expression ((3)/(2))^(3), (3/2) is the base raised to the exponent 3. Base: 3/2 Exponent: 3Choose expanded form: Choose the expanded form of ((3)/(2))^(3). The base is 3/2 and the exponent is 3. So, ((3)/(2))^(3) means (3/2) is multiplied by itself 3 times. Expanded Form of ((3)/(2))^(3): (3/2) × (3/2) × (3/2)Multiply to simplest form: ((3)/(2))^(3) = (3/2) × (3/2) × (3/2) Multiply to write in simplest form. ((3)/(2))^(3) = (3/2) × (3/2) × (3/2) = (3 × 3 × 3) / (2 × 2 × 2) = 27/8 The simplest form of ((3)/(2))^(3) is 27/8.

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Math Problems

Grade 8

Powers with negative bases

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Q. Evaluate.

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

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $\left(\frac{3}{2}\right)^{3}$ , $\frac{3}{2}$ is the base raised to the exponent $3$ . $\newline$ Base: $\frac{3}{2}$ $\newline$ Exponent: $3$
Choose expanded form: Choose the expanded form of $((3)/(2))^3$ . $\newline$ The base is $\frac{3}{2}$ and the exponent is $3$ . $\newline$ So, $\left(\frac{3}{2}\right)^3$ means $\frac{3}{2}$ is multiplied by itself $3$ times. $\newline$ Expanded Form of $\left(\frac{3}{2}\right)^3$ : $\newline$ $\frac{3}{2} \times \frac{3}{2} \times \frac{3}{2}$
Multiply to simplest form: $(\frac{3}{2})^{3} = (\frac{3}{2}) \times (\frac{3}{2}) \times (\frac{3}{2})$ $\newline$ Multiply to write in simplest form. $\newline$ $(\frac{3}{2})^{3}$ $\newline$ $= (\frac{3}{2}) \times (\frac{3}{2}) \times (\frac{3}{2})$ $\newline$ $= (3 \times 3 \times 3) / (2 \times 2 \times 2)$ $\newline$ $= \frac{27}{8}$ $\newline$ The simplest form of $(\frac{3}{2})^{3}$ is $\frac{27}{8}$ .