Evaluate. (-1(2)/(3))^(2)=

Identify base and exponent: Identify the base and the exponent. In the expression (-1(2)/(3))^2, -1(2)/(3) is the base raised to the exponent 2. Base: -1(2)/(3) Exponent: 2Choose expanded form: Choose the expanded form of (-1(2)/(3))^2. The base is -1(2)/(3) and the exponent is 2. So, (-1(2)/(3))^2 means -1(2)/(3) is multiplied by itself 2 times. Expanded Form of (-1(2)/(3))^2: (-1(2)/(3)) × (-1(2)/(3))Calculate product: (-1(2)/(3))^2 = (-1(2)/(3)) × (-1(2)/(3)) Multiply to write in simplest form. First, we need to understand that -1(2)/(3) is the same as -1 + (2)/(3) or -(1 + (2)/(3)). So, (-1(2)/(3))^2 = (-1 + (2)/(3)) × (-1 + (2)/(3)) = (-1 + (2)/(3)) × (-1 + (2)/(3))Simplify expression: Calculate the product. (-1 + (2)/(3)) × (-1 + (2)/(3)) = 1 - (2)/(3) - (2)/(3) + (2/3)(2/3) = 1 - (4)/(3) + (4)/(9)Simplify the expression. 1 - (4)/(3) + (4)/(9) To combine these terms, we need a common denominator, which is 9. = (9)/(9) - (12)/(9) + (4)/(9) = (9 - 12 + 4)/(9) = (1)/(9)

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Evaluate. $\newline$ $\left(-1 \frac{2}{3}\right)^{2}=$

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Grade 8

Powers with negative bases

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Q. Evaluate.

\newline

\left(-1 \frac{2}{3}\right)^{2}=

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $(-1(2)/(3))^2$ , $-1(2)/(3)$ is the base raised to the exponent $2$ . $\newline$ Base: $-1(2)/(3)$ $\newline$ Exponent: $2$
Choose expanded form: Choose the expanded form of $(-1\left(\frac{2}{3}\right))^2$ . The base is $-1\left(\frac{2}{3}\right)$ and the exponent is $2$ . So, $(-1\left(\frac{2}{3}\right))^2$ means $-1\left(\frac{2}{3}\right)$ is multiplied by itself $2$ times. Expanded Form of $(-1\left(\frac{2}{3}\right))^2$ : $(-1\left(\frac{2}{3}\right)) \times (-1\left(\frac{2}{3}\right))$
Calculate product: $(-1(2)/(3))^2 = (-1(2)/(3)) \times (-1(2)/(3))$ $\newline$ Multiply to write in simplest form. $\newline$ First, we need to understand that $-1(2)/(3)$ is the same as $-1 + (2)/(3)$ or $-(1 + (2)/(3))$ . $\newline$ So, $(-1(2)/(3))^2$ $\newline$ = $(-1 + (2)/(3)) \times (-1 + (2)/(3))$ $\newline$ = $(-1 + (2)/(3)) \times (-1 + (2)/(3))$
Simplify expression: Calculate the product. $\newline$ $(-1 + \frac{2}{3}) \times (-1 + \frac{2}{3})$ $\newline$ $= 1 - \frac{2}{3} - \frac{2}{3} + (\frac{2}{3})(\frac{2}{3})$ $\newline$ $= 1 - \frac{4}{3} + \frac{4}{9}$
Simplify expression: Calculate the product. $\newline$ $(-1 + \frac{2}{3}) \times (-1 + \frac{2}{3})$ $\newline$ $= 1 - \frac{2}{3} - \frac{2}{3} + (\frac{2}{3})(\frac{2}{3})$ $\newline$ $= 1 - \frac{4}{3} + \frac{4}{9}$ Simplify the expression. $\newline$ $1 - \frac{4}{3} + \frac{4}{9}$ $\newline$ To combine these terms, we need a common denominator, which is $9$ . $\newline$ $= \frac{9}{9} - \frac{12}{9} + \frac{4}{9}$ $\newline$ $= \frac{9 - 12 + 4}{9}$ $\newline$ $= \frac{1}{9}$