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Select the correct answer.

Simplify the following expression:
[tex]\[5^{-3}\][/tex]

A. [tex]\(-\frac{1}{5^3}\)[/tex]

B. [tex]\(-5^3\)[/tex]

C. [tex]\(5(-3)\)[/tex]

D. [tex]\(\frac{1}{5^3}\)[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\( 5^{-3} \)[/tex], we need to understand the rules of exponents, particularly the rule for negative exponents. The rule states that:

[tex]\[ a^{-n} = \frac{1}{a^n} \][/tex]

For our expression [tex]\( 5^{-3} \)[/tex], we apply this rule.

[tex]\[ 5^{-3} = \frac{1}{5^3} \][/tex]

Now, let's calculate [tex]\( 5^3 \)[/tex]:

[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]

Therefore:

[tex]\[ 5^{-3} = \frac{1}{125} \][/tex]

Comparing this result to the choices given, we find that the correct choice is:

D. [tex]\( \frac{1}{5^3} \)[/tex]

Thus, the simplified form of the expression [tex]\( 5^{-3} \)[/tex] is [tex]\( \frac{1}{5^3} \)[/tex], and the correct answer is option D.
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