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 Simplify: (-(2)/(5))^(2) = (-(2)/(5)) × (-(2)/(5)) Multiply to write in simplest form. (-(2)/(5))^(2) = (-(2)/(5)) × (-(2)/(5)) = (2/5) × (2/5) = (2 × 2) / (5 × 5) = 4 / 25 The simplest form of (-(2)/(5))^(2) is 4/25.

Home

Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

\newline

\left(-\frac{2}{5}\right)^{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 $\left(-\frac{2}{5}\right)^{2}$ . The base is $-\frac{2}{5}$ and the exponent is $2$ . So, $\left(-\frac{2}{5}\right)^{2}$ means $-\frac{2}{5}$ is multiplied by itself $2$ times. Expanded Form of $\left(-\frac{2}{5}\right)^{2}$ : $\left(-\frac{2}{5}\right) \times \left(-\frac{2}{5}\right)$
Multiply to Simplify: $(-\frac{2}{5})^{2} = (-\frac{2}{5}) \times (-\frac{2}{5})$ $\newline$ Multiply to write in simplest form. $\newline$ $(-\frac{2}{5})^{2}$ $\newline$ $= (-\frac{2}{5}) \times (-\frac{2}{5})$ $\newline$ $= \frac{2}{5} \times \frac{2}{5}$ $\newline$ $= \frac{2 \times 2}{5 \times 5}$ $\newline$ $= \frac{4}{25}$ $\newline$ The simplest form of $(-\frac{2}{5})^{2}$ is $\frac{4}{25}$ .