Answered

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Which expression is equivalent to [tex]$(10x)^{-3}$[/tex]?

A. [tex]\frac{10}{x^3}[/tex]
B. [tex]\frac{1000}{x^3}[/tex]
C. [tex]\frac{1}{1000 x^3}[/tex]
D. [tex]\frac{1}{10 x^3}[/tex]

Sagot :

GinnyAnswer
To determine which expression is equivalent to [tex]\((10x)^{-3}\)[/tex], we need to simplify [tex]\((10x)^{-3}\)[/tex] step-by-step using the properties of exponents.

1. Rewrite the expression using the negative exponent property:
[tex]\[ (10x)^{-3} = \frac{1}{(10x)^3} \][/tex]

2. Expand the denominator:
[tex]\[ (10x)^3 = 10^3 \cdot x^3 \][/tex]

3. Calculate [tex]\(10^3\)[/tex]:
[tex]\[ 10^3 = 10 \times 10 \times 10 = 1000 \][/tex]

4. Substitute back into the expression:
[tex]\[ \frac{1}{(10x)^3} = \frac{1}{1000 \cdot x^3} \][/tex]

So, [tex]\((10x)^{-3}\)[/tex] is equivalent to [tex]\(\frac{1}{1000 x^3}\)[/tex].

The correct equivalent expression among the given options is:

[tex]\[ \frac{1}{1000 x^3} \][/tex]
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