SOLUTION: Hello tutors: base 8 ^ 5/3 = 2^(4 x/2).....I got the first half by doing this...base (2^3)^5/3 and then base 2^5... the second part I could not figure that out...can I have a ste

Algebra ->  Exponents -> SOLUTION: Hello tutors: base 8 ^ 5/3 = 2^(4 x/2).....I got the first half by doing this...base (2^3)^5/3 and then base 2^5... the second part I could not figure that out...can I have a ste      Log On


   



Question 981158: Hello tutors: base 8 ^ 5/3
= 2^(4 x/2).....I got the first half by doing this...base (2^3)^5/3 and then base 2^5... the second part I could not figure that out...can I have a step by step on the second part of this equation and final answer...thanks tutors.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!


Simplify the exponent %284x%29%2F2 as just 2x



Next, write 8 as 2%5E3



Next, we multiply the exponents of 2 on the left 3%2Aexpr%285%2F3%29 getting 5

matrix%281%2C3%2C2%5E5%2C%22%22=%22%22%2C2%5E%282x%29+%29

Now that the bases are the same on both sides and they are 2, 
which is positive and not 1, we merely equate the exponents
of 2:

matrix%281%2C3%2C5%2C%22%22=%22%22%2C2x%29

matrix%281%2C3%2C5%2F2%2C%22%22=%22%22%2Cx%29

Edwin