Identify Base and Exponent: Identify the base and the exponent. In the expression -4^3, 4 is the base raised to the exponent 3, and the negative sign is outside the exponentiation. Base: 4 Exponent: 3 Negative Sign: Outside the exponentiationChoose Expanded Form: Choose the expanded form of -4^3. The base is 4 and the exponent is 3. The negative sign applies to the whole expression. So, -4^3 means -1 times 4 multiplied by itself 3 times. Expanded Form of -4^3: -1 × 4 × 4 × 4Multiply to Simplify: -4^3 = -1 × 4 × 4 × 4 Multiply to write in simplest form. -4^3 = -1 × 4 × 4 × 4 = -1 × 16 × 4 = -1 × 64 = -64 The simplest form of -4^3 is -64.

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

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-4^{3}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $-4^3$ , $4$ is the base raised to the exponent $3$ , and the negative sign is outside the exponentiation. $\newline$ Base: $4$ $\newline$ Exponent: $3$ $\newline$ Negative Sign: Outside the exponentiation
Choose Expanded Form: Choose the expanded form of $-4^3$ . The base is $4$ and the exponent is $3$ . The negative sign applies to the whole expression. So, $-4^3$ means $-1$ times $4$ multiplied by itself $3$ times. Expanded Form of $-4^3$ : $-1 \times 4 \times 4 \times 4$
Multiply to Simplify: $-4^3 = -1 \times 4 \times 4 \times 4$ $\newline$ Multiply to write in simplest form. $\newline$ $-4^3$ $\newline$ $= -1 \times 4 \times 4 \times 4$ $\newline$ $= -1 \times 16 \times 4$ $\newline$ $= -1 \times 64$ $\newline$ $= -64$ $\newline$ The simplest form of $-4^3$ is $-64$ .