Identify Base and Exponent: Identify the base and the exponent. In the expression (-3)^4, -3 is the base raised to the exponent 4. Base: -3 Exponent: 4Choose Expanded Form: Choose the expanded form of (-3)^4. The base is -3 and the exponent is 4. So, (-3)^4 means -3 is multiplied by itself 4 times. Expanded Form of (-3)^4: (-3) × (-3) × (-3) × (-3)Multiply for Simplest Form: Multiply to write in simplest form. (-3)^4 = (-3) × (-3) × (-3) × (-3) = 9 × (-3) × (-3) // Multiplying the first two -3s gives us 9 = 9 × 9 // Multiplying the next two -3s also gives us 9 = 81 // Multiplying 9 by 9 gives us 81

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

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(-3)^{4}=

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $(-3)^4$ , $-3$ is the base raised to the exponent $4$ . $\newline$ Base: $-3$ $\newline$ Exponent: $4$
Choose Expanded Form: Choose the expanded form of $(-3)^4$ . The base is $-3$ and the exponent is $4$ . So, $(-3)^4$ means $-3$ is multiplied by itself $4$ times. Expanded Form of $(-3)^4$ : $(-3) \times (-3) \times (-3) \times (-3)$
Multiply for Simplest Form: Multiply to write in simplest form. $\newline$ $(-3)^4$ $\newline$ = $(-3) \times (-3) \times (-3) \times (-3)$ $\newline$ = $9 \times (-3) \times (-3)$ // Multiplying the first two $-3$ s gives us $9$ $\newline$ = $9 \times 9$ // Multiplying the next two $-3$ s also gives us $9$ $\newline$ = $81$ // Multiplying $9$ by $9$ gives us $81$