Mathematics
wzyromero
11

If 3x-y=123x−y=123, x, minus, y, equals, 12, what is the value of \dfrac{8^x}{2^y} ​2 ​y ​​ ​ ​8 ​x ​​ ​​ start fraction, 8, start superscript, x, end superscript, divided by, 2, start superscript, y, end superscript, end fraction ?

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(1) Answers
Mireille708

We are given the equation: 3x – y = 12                           ---> 1 And we are asked to find for the value of: 8^x / 2^y = ?                      ---> 2   To solve this problem easily, we start with the equation 2: 8^x / 2^y First, we know that: 8 = 2 x 2 x 2 = 2^3 So this makes equation 2 into: 8^x / 2^y = 2^3x / 2^y When the bases are similar and the bases are divided, then the exponents get subtracted. Therefore: 2^3x / 2^y = 2^(3x – 2y) Now it was given from equation that: 3x – y = 12               Therefore: 2^(3x – 2y) = 2^12 = 8^x / 2^y   Answer: 8^x / 2^y = 2^12 = 4096

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