Identify Base and Exponent: Identify the base and the exponent. In the expression -3^3, 3 is the base raised to the exponent 3, and the negative sign is outside the exponentiation. Base: 3 Exponent: 3 Negative Sign: Outside the exponentiationChoose Expanded Form: Choose the expanded form of -3^3. The base is 3 and the exponent is 3. The negative sign applies to the whole expression, not just the base. So, -3^3 means 3 is multiplied by itself 3 times, and then the negative sign is applied. Expanded Form of -3^3: - (3 × 3 × 3)Calculate Value of 3^3: Calculate the value of 3^3. 3^3 = 3 × 3 × 3 = 9 × 3 = 27Apply Negative Sign: Apply the negative sign to the result of 3^3. -3^3 = - (27) = -27

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

\newline

-3^{3}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $-3^3$ , $3$ is the base raised to the exponent $3$ , and the negative sign is outside the exponentiation. $\newline$ Base: $3$ $\newline$ Exponent: $3$ $\newline$ Negative Sign: Outside the exponentiation
Choose Expanded Form: Choose the expanded form of $-3^3$ . The base is $3$ and the exponent is $3$ . The negative sign applies to the whole expression, not just the base. So, $-3^3$ means $3$ is multiplied by itself $3$ times, and then the negative sign is applied. Expanded Form of $-3^3$ : $- (3 \times 3 \times 3)$
Calculate Value of $3^3$ : Calculate the value of $3^3$ . $\newline$ $3^3$ $\newline$ = $3 \times 3 \times 3$ $\newline$ = $9 \times 3$ $\newline$ = $27$
Apply Negative Sign: Apply the negative sign to the result of $3^3$ . $\newline$ $-3^3$ $\newline$ $= - (27)$ $\newline$ $= -27$