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

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

Home

Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

\newline

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

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $(-2(2)/(3))^{2}$ , $-2(2)/(3)$ is the base raised to the exponent $2$ . $\newline$ Base: $-2(2)/(3)$ $\newline$ Exponent: $2$
Choose expanded form: Choose the expanded form of $(-2(2)/(3))^{2}$ . $\newline$ The base is $-2(2)/(3)$ and the exponent is $2$ . $\newline$ So, $(-2(2)/(3))^{2}$ means $-2(2)/(3)$ is multiplied by itself once. $\newline$ Expanded Form of $(-2(2)/(3))^{2}$ : $\newline$ $(-2(2)/(3)) \times (-2(2)/(3))$
Multiply to simplify: $(-2(2)/(3))^{2} = (-2(2)/(3)) \times (-2(2)/(3))$ $\newline$ Multiply to write in simplest form. $\newline$ First, simplify the base: $-2(2)/(3) = -4/3$ $\newline$ Now, $(-4/3)^{2} = (-4/3) \times (-4/3)$
Final answer: $(-\frac{4}{3}) \times (-\frac{4}{3}) = \frac{16}{9}$ $\newline$ When multiplying two negative numbers, the result is positive. $\newline$ So, the simplest form of $(-2(\frac{2}{3}))^{2}$ is $\frac{16}{9}$ .