Which is equal to 4^-3? Choices: (A)-(-4)^3 (B)1/4^3 (C)(-4)^-3 (D)4^3

Understand expression 4^-3: Step 1: Understand the expression 4^-3. Rewrite 4^-3 using the property of negative exponents, which states that a^-n = 1/a^n. Calculation: 4^-3 = 1/4^3 Rewrite using negative exponents: Step 2: Match the rewritten expression with the given choices. From Step 1, we have 4^-3 = 1/4^3. Check each choice: (A) -(-4)^3 = -(-64) = 64, not equal to 1/4^3. (B) 1/4^3 = 1/64, matches our calculation. (C) (-4)^-3 = 1/(-4)^3 = 1/(-64), not equal to 1/4^3. (D) 4^3 = 64, not equal to 1/4^3.

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Which is equal to $4^{-3}$ ? $\newline$ Choices: $\newline$ (A) $-(-4)^3$ $\newline$ (B) $\frac{1}{4^3}$ $\newline$ (C) $(-4)^{-3}$ $\newline$ (D) $4^3$

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Math Problems

Grade 8

Understanding negative exponents

Full solution

Q. Which is equal to

4^{-3}

\newline

Choices:

\newline

(A)

-(-4)^3

\newline

(B)

\frac{1}{4^3}

\newline

(C)

(-4)^{-3}

\newline

(D)

4^3

Understand expression $4^{-3}$ : Step $1$ : Understand the expression $4^{-3}$ . Rewrite $4^{-3}$ using the property of negative exponents, which states that $a^{-n} = \frac{1}{a^n}$ . Calculation: $4^{-3} = \frac{1}{4^3}$
Rewrite using negative exponents: Step $2$ : Match the rewritten expression with the given choices. $\newline$ From Step $1$ , we have $4^{-3} = 1/4^3$ . $\newline$ Check each choice: $\newline$ (A) $-(-4)^3 = -(-64) = 64$ , not equal to $1/4^3$ . $\newline$ (B) $1/4^3 = 1/64$ , matches our calculation. $\newline$ (C) $(-4)^{-3} = 1/(-4)^3 = 1/(-64)$ , not equal to $1/4^3$ . $\newline$ (D) $4^3 = 64$ , not equal to $1/4^3$ .