Solved on Dec 05, 2023

Simplify the expression $(-8)^{-2}$ without using an exponent.

STEP 1

Assumptions
1. The given expression is $(-8)^{-2}$ .
2. A negative exponent indicates that the base should be taken as the reciprocal and the exponent made positive.

STEP 2

Understand the meaning of a negative exponent. For any nonzero number $a$ and positive integer $n$ , $a^{-n}$ is defined as:
$a^{-n} = \frac{1}{a^n}$

STEP 3

Apply the negative exponent rule to the given expression.
$(-8)^{-2} = \frac{1}{(-8)^2}$

STEP 4

Calculate the square of $-8$ .
$(-8)^2 = (-8) \times (-8)$

STEP 5

Perform the multiplication to find the square.
$(-8)^2 = 64$

STEP 6

Now, substitute the result back into the expression with the reciprocal.
$\frac{1}{(-8)^2} = \frac{1}{64}$
The expression $(-8)^{-2}$ rewritten without an exponent is $\frac{1}{64}$ .

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Simplify the expression $(-8)^{-2}$ without using an exponent.

STEP 1

Assumptions
1. The given expression is $(-8)^{-2}$ .
2. A negative exponent indicates that the base should be taken as the reciprocal and the exponent made positive.

STEP 2

Understand the meaning of a negative exponent. For any nonzero number $a$ and positive integer $n$ , $a^{-n}$ is defined as:
$a^{-n} = \frac{1}{a^n}$

STEP 3

Apply the negative exponent rule to the given expression.
$(-8)^{-2} = \frac{1}{(-8)^2}$

STEP 4

Calculate the square of $-8$ .
$(-8)^2 = (-8) \times (-8)$

STEP 5

Perform the multiplication to find the square.
$(-8)^2 = 64$

STEP 6

Now, substitute the result back into the expression with the reciprocal.
$\frac{1}{(-8)^2} = \frac{1}{64}$
The expression $(-8)^{-2}$ rewritten without an exponent is $\frac{1}{64}$ .

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Simplify the expression (−8)−2(-8)^{-2}(−8)−2 without using an exponent.

STEP 1

Assumptions1. The given expression is (−8)−2(-8)^{-2}(−8)−2.2. A negative exponent indicates that the base should be taken as the reciprocal and the exponent made positive.

STEP 2

Understand the meaning of a negative exponent. For any nonzero number aaa and positive integer nnn, a−na^{-n}a−n is defined as:a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1​

STEP 3

Apply the negative exponent rule to the given expression.(−8)−2=1(−8)2(-8)^{-2} = \frac{1}{(-8)^2}(−8)−2=(−8)21​

STEP 4

Calculate the square of −8-8−8.(−8)2=(−8)×(−8)(-8)^2 = (-8) \times (-8)(−8)2=(−8)×(−8)

STEP 5

Perform the multiplication to find the square.(−8)2=64(-8)^2 = 64(−8)2=64

STEP 6

Now, substitute the result back into the expression with the reciprocal.1(−8)2=164\frac{1}{(-8)^2} = \frac{1}{64}(−8)21​=641​The expression (−8)−2(-8)^{-2}(−8)−2 rewritten without an exponent is 164\frac{1}{64}641​.

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Simplify the expression $(-8)^{-2}$ without using an exponent.

Assumptions
1. The given expression is $(-8)^{-2}$ .
2. A negative exponent indicates that the base should be taken as the reciprocal and the exponent made positive.

Understand the meaning of a negative exponent. For any nonzero number $a$ and positive integer $n$ , $a^{-n}$ is defined as:
$a^{-n} = \frac{1}{a^n}$

Apply the negative exponent rule to the given expression.
$(-8)^{-2} = \frac{1}{(-8)^2}$

Calculate the square of $-8$ .
$(-8)^2 = (-8) \times (-8)$

Perform the multiplication to find the square.
$(-8)^2 = 64$

Now, substitute the result back into the expression with the reciprocal.
$\frac{1}{(-8)^2} = \frac{1}{64}$
The expression $(-8)^{-2}$ rewritten without an exponent is $\frac{1}{64}$ .