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

Identify base and exponent: Identify the base and the exponent. In the expression (-(3)/(2))^(4), -(3)/(2) is the base raised to the exponent 4. Base: -(3)/(2) Exponent: 4Choose expanded form: Choose the expanded form of (-(3)/(2))^(4). The base is -(3)/(2) and the exponent is 4. So, (-(3)/(2))^(4) means -(3)/(2) is multiplied by itself 4 times. Expanded Form of (-(3)/(2))^(4): (-(3)/(2)) × (-(3)/(2)) × (-(3)/(2)) × (-(3)/(2))Multiply to simplify: (-(3)/(2))^(4) = (-(3)/(2)) × (-(3)/(2)) × (-(3)/(2)) × (-(3)/(2)) Multiply to write in simplest form. When multiplying two negative numbers, the result is positive. So, (-(3)/(2)) × (-(3)/(2)) = (3/2) × (3/2) = 9/4Multiply result from Step 3: Now multiply the result from Step 3 by (-(3)/(2)) twice. (9/4) × (-(3)/(2)) × (-(3)/(2)) Again, multiplying two negative numbers gives a positive result. (9/4) × (3/2) × (3/2) = (9/4) × (9/4) = 81/16

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

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Math Problems

Grade 8

Powers with negative bases

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Q. Evaluate.

\newline

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

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $\left(-\frac{3}{2}\right)^{4}$ , $-\frac{3}{2}$ is the base raised to the exponent $4$ . $\newline$ Base: $-\frac{3}{2}$ $\newline$ Exponent: $4$
Choose expanded form: Choose the expanded form of $\left(-\frac{3}{2}\right)^{4}$ . The base is $-\frac{3}{2}$ and the exponent is $4$ . So, $\left(-\frac{3}{2}\right)^{4}$ means $-\frac{3}{2}$ is multiplied by itself $4$ times. Expanded Form of $\left(-\frac{3}{2}\right)^{4}$ : $\left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right)$
Multiply to simplify: $\left(-\frac{3}{2}\right)^{4} = \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right)$ $\newline$ Multiply to write in simplest form. $\newline$ When multiplying two negative numbers, the result is positive. $\newline$ So, $\left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) = \left(\frac{3}{2}\right) \times \left(\frac{3}{2}\right) = \frac{9}{4}$
Multiply result from Step $3$ : Now multiply the result from Step $3$ by $\left(-\frac{3}{2}\right)$ twice. $\newline$ $\left(\frac{9}{4}\right) \times \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right)$ $\newline$ Again, multiplying two negative numbers gives a positive result. $\newline$ $\left(\frac{9}{4}\right) \times \left(\frac{3}{2}\right) \times \left(\frac{3}{2}\right) = \left(\frac{9}{4}\right) \times \left(\frac{9}{4}\right) = \frac{81}{16}$