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notsponge [240]
3 years ago
8

Carolyn's house is 15 miles south of Ben's

Mathematics
1 answer:
Jlenok [28]3 years ago
6 0

Answer:

17

Step-by-step explanation:

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Which of the following is equivalent to (125^2/ 125^4/3)
zysi [14]

Option D:

The expression equivalent to the given expression is 25.

Solution:

The image of the question is attached below.

Given expression:

$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)

To find which expression is equivalent to the given expression:

$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)

125 can be written as 5 × 5 × 5 = 5³

      $=\frac{(5^3)^{2}}{(5^3)^{\frac{4}{3}}}

Using the exponent rule: \left(a^{m}\right)^{n}=a^{(m n)}

     $=\frac{5^6}{5^{\frac{12}{3}}}

     $=\frac{5^6}{5^4}

Using the exponent rule: \frac{a^{m}}{a^{n}}=a^{m-n}

      =5^{(6-4)}

      = 5²

      = 25

$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)=25

The expression equivalent to the given expression is 25.

Option D is the correct answer.

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