Identify Base and Exponent: Identify the base and the exponent. In the expression (-2)^3, -2 is the base raised to the exponent 3. Base: -2 Exponent: 3Choose Expanded Form: Choose the expanded form of (-2)^3. The base is -2 and the exponent is 3. So, (-2)^3 means -2 is multiplied by itself 3 times. Expanded Form of (-2)^3: (-2) × (-2) × (-2)Multiply to Simplify: (-2)^3 = (-2) × (-2) × (-2) Multiply to write in simplest form. (-2)^3 = (-2) × (-2) × (-2) = 4 × (-2) = -8 The simplest form of (-2)^3 is -8.

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

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(-2)^{3}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $(-2)^3$ , $-2$ is the base raised to the exponent $3$ . $\newline$ Base: $-2$ $\newline$ Exponent: $3$
Choose Expanded Form: Choose the expanded form of $(-2)^3$ . The base is $-2$ and the exponent is $3$ . So, $(-2)^3$ means $-2$ is multiplied by itself $3$ times. Expanded Form of $(-2)^3$ : $(-2) \times (-2) \times (-2)$
Multiply to Simplify: $(-2)^3 = (-2) \times (-2) \times (-2)$ $\newline$ Multiply to write in simplest form. $\newline$ $(-2)^3$ $\newline$ $= (-2) \times (-2) \times (-2)$ $\newline$ $= 4 \times (-2)$ $\newline$ $= -8$ $\newline$ The simplest form of $(-2)^3$ is $-8$ .