Identify Base and Exponent: Identify the base and the exponent. In the expression -2^5, 2 is the base and 5 is the exponent. However, the negative sign is not included in the base, it is outside the exponentiation. Base: 2 Exponent: 5 Negative sign: Outside the baseChoose 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 × 2Calculate 2^5: Calculate 2^5. 2^5 = 2 × 2 × 2 × 2 × 2 = 4 × 2 × 2 × 2 = 8 × 2 × 2 = 16 × 2 = 32 The value of 2^5 is 32.Apply Negative Sign: Apply the negative sign to the result of 2^5. Since the negative sign is outside the exponentiation, it applies to the whole expression, making the result negative. -2^5 = -32

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

\newline

-2^{5}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $-2^5$ , $2$ is the base and $5$ is the exponent. However, the negative sign is not included in the base, it is outside the exponentiation. $\newline$ Base: $2$ $\newline$ Exponent: $5$ $\newline$ Negative sign: Outside the base
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 $2^5$ : $2 \times 2 \times 2 \times 2 \times 2$
Calculate $2^5$ : Calculate $2^5$ . $\newline$ $2^5$ $\newline$ $= 2 \times 2 \times 2 \times 2 \times 2$ $\newline$ $= 4 \times 2 \times 2 \times 2$ $\newline$ $= 8 \times 2 \times 2$ $\newline$ $= 16 \times 2$ $\newline$ $= 32$ $\newline$ The value of $2^5$ is $32$ .
Apply Negative Sign: Apply the negative sign to the result of $2^5$ . Since the negative sign is outside the exponentiation, it applies to the whole expression, making the result negative. $-2^5 = -32$