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Mila [183]
3 years ago
10

(64/125) to the power of -2/3

Mathematics
1 answer:
Sedaia [141]3 years ago
7 0
As the exponent is negative, we can rewrite the expression as (125/64) raised to the power 2/3.

So, (125/64) raised to the power 2/3 can also be written as [(5/4) raised to the power 3] raised to the power 2/3. The exponents will multiply and the final exponent will be 2.

Hence the answer will be (5/4) squared.
Therefore the answer is (24/16).
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Isabella went into a movie theater and bought 3 drinks and 10 pretzels, costing a total of $54.50. Jason went into the same movi
ruslelena [56]

The price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25

<em><u>Solution:</u></em>

Let d" be the price of 1 drink

Let "p" be the price of 1 pretzel

Given that, Isabella went into a movie theater and bought 3 drinks and 10 pretzels, costing a total of $54.50

<em><u>Therefore, we can frame a equation as,</u></em>

3 x price of 1 drink + 10 x price of 1 pretzel = 54.50

3 \times d + 10 \times p = 54.50

3d + 10p = 54.5 ---------- eqn 1

Jason went into the same movie theater and bought 9 drinks and 5 pretzels, costing a total of $57.25

9 x price of 1 drink + 5 x price of 1 pretzel = 57.25

9 \times d + 5 \times p = 57.25

9d + 5p = 57.25 ---------- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

Multiply eqn 1 by 3

9d + 30p = 163.5 ----- eqn 3

<em><u>Subtract eqn 2 from eqn 3</u></em>

9d + 30p = 163.5

9d + 5p = 57.25

( - ) -----------------------

25p = 106.25

p = 4.25

<em><u>Substitute p = 4.25 in eqn 1</u></em>

3d + 10(4.25) = 54.5

3d + 42.5 = 54.5

3d = 54.5 - 42.5

3d = 12

d = 4

Thus price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25

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Answer:

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Step-by-step explanation:

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