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

Identify Base and Exponent: Identify the base and the exponent. In the expression (-2(2)/(5))^(2), -2(2)/(5) is the base raised to the exponent 2. Base: -2(2)/(5) Exponent: 2Simplify Base: Simplify the base before applying the exponent. The base -2(2)/(5) can be simplified by multiplying -2 by (2)/(5). Simplified Base: -2 * (2)/(5) = -4/5Apply Exponent: Apply the exponent to the simplified base. Now that we have the simplified base, we can raise it to the power of 2. (-4/5)^(2) means (-4/5) is multiplied by itself once. Expanded Form of (-4/5)^(2): (-4/5) × (-4/5)Multiply for Simplest Form: Multiply to write in simplest form. (-4/5) × (-4/5) = (16/25) When multiplying two negative numbers, the result is positive.

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Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

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

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $(-2(2)/(5))^{2}$ , $-2(2)/(5)$ is the base raised to the exponent $2$ . $\newline$ Base: $-2(2)/(5)$ $\newline$ Exponent: $2$
Simplify Base: Simplify the base before applying the exponent. $\newline$ The base $-2\left(\frac{2}{5}\right)$ can be simplified by multiplying $-2$ by $\left(\frac{2}{5}\right)$ . $\newline$ Simplified Base: $-2 \times \left(\frac{2}{5}\right) = -\frac{4}{5}$
Apply Exponent: Apply the exponent to the simplified base. $\newline$ Now that we have the simplified base, we can raise it to the power of $2$ . $\newline$ $(-\frac{4}{5})^{2}$ means $(-\frac{4}{5})$ is multiplied by itself once. $\newline$ Expanded Form of $(-\frac{4}{5})^{2}$ : $\newline$ $(-\frac{4}{5}) \times (-\frac{4}{5})$
Multiply for Simplest Form: Multiply to write in simplest form. $\newline$ $(-\frac{4}{5}) \times (-\frac{4}{5}) = \frac{16}{25}$ $\newline$ When multiplying two negative numbers, the result is positive.