Identify Base and Exponent: Identify the base and the exponent. In the expression -2^3, 2 is the base raised to the exponent 3, and the negative sign is outside the exponentiation. Base: 2 Exponent: 3 Negative Sign: Outside the exponentiationChoose Expanded Form: Choose the expanded form of -2^3. The base is 2 and the exponent is 3. The negative sign applies to the whole expression. So, -2^3 means 2 is multiplied by itself 3 times, and then the negative sign is applied. Expanded Form of -2^3: - (2 × 2 × 2)Calculate Value of 2^3: Calculate the value of 2^3. 2^3 = 2 × 2 × 2 = 4 × 2 = 8Apply Negative Sign: Apply the negative sign to the result of 2^3. -2^3 = - (8) = -8

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

\newline

-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 $3$ , and the negative sign is outside the exponentiation. $\newline$ Base: $2$ $\newline$ Exponent: $3$ $\newline$ Negative Sign: Outside the exponentiation
Choose Expanded Form: Choose the expanded form of $-2^3$ . The base is $2$ and the exponent is $3$ . The negative sign applies to the whole expression. So, $-2^3$ means $2$ is multiplied by itself $3$ times, and then the negative sign is applied. Expanded Form of $-2^3$ : $- (2 \times 2 \times 2)$
Calculate Value of $2^3$ : Calculate the value of $2^3$ . $\newline$ $2^3$ $\newline$ = $2 \times 2 \times 2$ $\newline$ = $4 \times 2$ $\newline$ = $8$
Apply Negative Sign: Apply the negative sign to the result of $2^3$ . $-2^3$ $= - (8)$ $= -8$