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Which statement is true about the value of the expression below?
(-2^(3))^(-2)
(A) It is between 0 and 1.
(B) It is less than -1.
(C) It is between -1 and 0 .
(D)It is greater than 1.

Which statement is true about the value of the expression below? $\newline$ $(-2^{3})^{-2}$ $\newline$ (A) It is between $0$ and $1$ . $\newline$ (B) It is less than $-1$ . $\newline$ (C) It is between $-1$ and $0$ . $\newline$ (D) It is greater than $1$ .

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Full solution

Q. Which statement is true about the value of the expression below?

\newline

(-2^{3})^{-2}

\newline

(A) It is between

0

and

1

.

\newline

(B) It is less than

-1

.

\newline

(C) It is between

-1

and

0

.

\newline

(D) It is greater than

1

.

Simplify Inside Parentheses: First, let's simplify the inside of the parentheses. $\newline$ $(-2^3) = -8$
Raise to Negative Power: Now, raise $-8$ to the power of $-2$ . $(-8)^{-2} = \frac{1}{(-8)^2}$
Calculate Square: Calculate the square of $-8$ . $(-8)^2 = 64$
Take Reciprocal: Now, take the reciprocal since it's raised to the power of $-2$ . $\frac{1}{64}$ is the final value.
Final Value: $\frac{1}{64}$ is a positive number and it's between $0$ and $1$ .

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