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

Identify base and exponent: Identify the base and the exponent. In the expression ((2)/(5))^(2), (2/5) is the base raised to the exponent 2. Base: 2/5 Exponent: 2Choose expanded form: Choose the expanded form of ((2)/(5))^(2). The base is 2/5 and the exponent is 2. So, ((2)/(5))^(2) means (2/5) is multiplied by itself 2 times. Expanded Form of ((2)/(5))^(2): (2/5) × (2/5)Multiply to simplest form: ((2)/(5))^(2) = (2/5) × (2/5) Multiply to write in simplest form. ((2)/(5))^(2) = (2/5) × (2/5) = (2 × 2) / (5 × 5) = 4 / 25 The simplest form of ((2)/(5))^(2) is 4/25.

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Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

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(\frac{2}{5})^{2}=

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $\left(\frac{2}{5}\right)^{2}$ , $\frac{2}{5}$ is the base raised to the exponent $2$ . $\newline$ Base: $\frac{2}{5}$ $\newline$ Exponent: $2$
Choose expanded form: Choose the expanded form of $\left(\frac{2}{5}\right)^{2}$ . $\newline$ The base is $\frac{2}{5}$ and the exponent is $2$ . $\newline$ So, $\left(\frac{2}{5}\right)^{2}$ means $\frac{2}{5}$ is multiplied by itself $2$ times. $\newline$ Expanded Form of $\left(\frac{2}{5}\right)^{2}$ : $\newline$ $\frac{2}{5} \times \frac{2}{5}$
Multiply to simplest form: $\left(\frac{2}{5}\right)^2 = \left(\frac{2}{5}\right) \times \left(\frac{2}{5}\right)$ $\newline$ Multiply to write in simplest form. $\newline$ $\left(\frac{2}{5}\right)^2$ $\newline$ $= \left(\frac{2}{5}\right) \times \left(\frac{2}{5}\right)$ $\newline$ $= \left(2 \times 2\right) / \left(5 \times 5\right)$ $\newline$ $= \frac{4}{25}$ $\newline$ The simplest form of $\left(\frac{2}{5}\right)^2$ is $\frac{4}{25}$ .