Math Help

h3ndu

Ok - so, I have a final tomorrow in math 108, intermediate algebra - I have an A in the class, and I just took the practice final online - I did well, but there was one problem that stuck me - I searched through all my notes and I couldn't find anything on it - help me please?

the problem - (125/8) [so, one hundred and twenty five over eight] to the -2/8 th power. The answer to the problem is 4/25 [four over twenty five].

If anyone could walk me through this I would be very appreciative.

Powerpuppies

first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). Now ( (X^m)^n) = X^(m*n), so X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

If so, X^(2/3) is best computed as X^(1/3)^2, so take the cuberoot and square it. So 125/8 to the -2/3 would be 8^(2/3) / 125^(2/3) = 2^2/5^2 = 4/25.

enlightenedbum

Sure that was the question? Because pretty sure that's wrong.

Anyway, for how to do that kind of thing:

1) What do you do with negative exponents?
2) What do you do with fractions raised to a power?

h3ndu

Powerpuppies wrote: »

first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

no - no, it was definetly (125/8) to the -2/8.

I just ... seeing it in line form kind of sucks.

''''''''''-2/8
125

---

8

that's the problem - and when I finished the web test it told me the answer was

4
---
25

Powerpuppies

h3ndu wrote: »

Powerpuppies wrote: »

first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

no - no, it was definetly (125/8) to the -2/8.

I just ... seeing it in line form kind of sucks.

''''''''''-2/8
125

---

8

that's the problem - and when I finished the web test it told me the answer was

4
---
25

I mean I dunno what to tell you man. The test is wrong. 125/8^(-2/3) is 4/25. 125/8^(-2/8) is not, plus what kind of math problem starts with easily reducible fractional exponents? Some sort of typo or something.

h3ndu

Powerpuppies wrote: »

h3ndu wrote: »

Powerpuppies wrote: »

first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

no - no, it was definetly (125/8) to the -2/8.

I just ... seeing it in line form kind of sucks.

''''''''''-2/8
125

---

8

that's the problem - and when I finished the web test it told me the answer was

4
---
25

I mean I dunno what to tell you man. The test is wrong. 125/8^(-2/3) is 4/25. 125/8^(-2/8) is not, plus what kind of math problem starts with easily reducible fractional exponents? Some sort of typo or something.

I must have misread it and then tried to solve. I can't imagine the test itself would be wrong. It has to be an error on my part. It is kind of late right now.

Thanks for your help.

SkyCaptain

Three and eights would look similar, so -2/3 could have looked like -2/8 to you.