(125a^8)^1/3

Question

I get an answer of 5a^8/3. I am not sure if this is correct. I multiplied the exponents 8 *1/3 to get 8/3. For the 125, I am not sure if I am looking to cube the number or looking for the square root of 125?

Answer 1

f(a) = (125a^8)^(1/3)

 

125 = 5*25 = 5*5*5 = 5^3

 

f(a) = ((5^3)(a^8))^(1/3)

 

(ab)^p = (a^p)*(b^p)

 

f(a) = ((5^3)^(1/3))*((a^8)^(1/3))

 

(a^m)^n = a^(mn)

 

f(a) = 5 a^(8/3)

 

K, the answer you found on your own is right;

Michael's answer of 5a^2 is wrong.

 

Michael fixed his answer, so we're all in synch now.

Answer 2

(125a⁸)^1/3=125^1/3(a⁸)^1/3=5a^8/3

To the 1/3 power means take the cube root.

Sorry Steve.

Answer 3

If you are allowed to leave the exponents in fraction form, the answer is:
5a^(8/3)
However, if the problem needs to be in radical form and simplified, here are the next steps. First we know that whatever we simplify "a" into, it is going to be multiplied by 5 when we are done. With that in mind, we now work on the fractional exponent. We change it to a radical, so it looks like this:
³√a⁸

We say: "The cube root of 'a' to the 8th power"
This means that we have a*a*a*a*a*a*a*a under a cube root sign. This means "how many a³ do we have in a*a*a*a*a*a*a*a?" The answer is two, with two left over. Our new problem looks like this:
2a*³√a²
Now we have to multiply this by five, from the beginning of the problem. When we do, our final answer is:
10a*³√a²