Identify Base and Exponent: Identify the base and the exponent. In the expression (-2)^5, -2 is the base raised to the exponent 5. Base: -2 Exponent: 5Choose Expanded Form: Choose the expanded form of (-2)^5. The base is -2 and the exponent is 5. So, (-2)^5 means -2 is multiplied by itself 5 times. Expanded Form of (-2)^5: (-2) × (-2) × (-2) × (-2) × (-2)Multiply for Simplest Form: Multiply to write in simplest form. (-2)^5 = (-2) × (-2) × (-2) × (-2) × (-2) = 4 × (-2) × (-2) × (-2) (Multiplying the first two -2s) = 4 × 4 × (-2) (Multiplying the next two -2s) = 16 × (-2) (Multiplying the last two numbers) = -32 (Multiplying 16 by -2)

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

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(-2)^{5}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $(-2)^5$ , $-2$ is the base raised to the exponent $5$ . $\newline$ Base: $-2$ $\newline$ Exponent: $5$
Choose Expanded Form: Choose the expanded form of $(-2)^5$ . The base is $-2$ and the exponent is $5$ . So, $(-2)^5$ means $-2$ is multiplied by itself $5$ times. Expanded Form of $(-2)^5$ : $(-2) \times (-2) \times (-2) \times (-2) \times (-2)$
Multiply for Simplest Form: Multiply to write in simplest form. $\newline$ $(-2)^5$ $\newline$ = $(-2) \times (-2) \times (-2) \times (-2) \times (-2)$ $\newline$ = $4 \times (-2) \times (-2) \times (-2)$ (Multiplying the first two $-2$ s) $\newline$ = $4 \times 4 \times (-2)$ (Multiplying the next two $-2$ s) $\newline$ = $16 \times (-2)$ (Multiplying the last two numbers) $\newline$ = $-32$ (Multiplying $16$ by $-2$ )