Evaluate. (-(5)/(3))^(2)=

Identify Base and Exponent: Identify the base and the exponent. In the expression (-(5)/(3))^(2), -(5/3) is the base raised to the exponent 2. Base: -(5/3) Exponent: 2Choose Expanded Form: Choose the expanded form of (-(5)/(3))^(2). The base is -(5/3) and the exponent is 2. So, (-(5)/(3))^(2) means -(5/3) is multiplied by itself once. Expanded Form of (-(5)/(3))^(2): (-(5)/(3)) × (-(5)/(3))Multiply to Simplify: (-(5)/(3))^(2) = (-(5)/(3)) × (-(5)/(3)) Multiply to write in simplest form. (-(5)/(3))^(2) = (-(5)/(3)) × (-(5)/(3)) = (25)/(9) The simplest form of (-(5)/(3))^(2) is (25)/(9).

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Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

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\left(-\frac{5}{3}\right)^{2}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $\left(-\frac{5}{3}\right)^{2}$ , $-\frac{5}{3}$ is the base raised to the exponent $2$ . $\newline$ Base: $-\frac{5}{3}$ $\newline$ Exponent: $2$
Choose Expanded Form: Choose the expanded form of $\left(-\frac{5}{3}\right)^{2}$ . The base is $-\frac{5}{3}$ and the exponent is $2$ . So, $\left(-\frac{5}{3}\right)^{2}$ means $-\frac{5}{3}$ is multiplied by itself once. Expanded Form of $\left(-\frac{5}{3}\right)^{2}$ : $\left(-\frac{5}{3}\right) \times \left(-\frac{5}{3}\right)$
Multiply to Simplify: $\left(-\frac{5}{3}\right)^{2} = \left(-\frac{5}{3}\right) \times \left(-\frac{5}{3}\right)$ $\newline$ Multiply to write in simplest form. $\newline$ $\left(-\frac{5}{3}\right)^{2}$ $\newline$ $= \left(-\frac{5}{3}\right) \times \left(-\frac{5}{3}\right)$ $\newline$ $= \frac{25}{9}$ $\newline$ The simplest form of $\left(-\frac{5}{3}\right)^{2}$ is $\frac{25}{9}$ .