Math Question

[Elysian12]

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I am getting confused with the concepts of fractional exponents. For example lets say I have 27^(4/3). I know you take the cube root and then do the 4th power or 4th power and then cube root it and you get the same answer. Here is where I am getting confused. A question on math destroyer asks to find the value of a. The problem is (a+3)^(4/3) = 16. However, if I cube root both sides and then do the 4th power to both sides to cancel the 4/3 out, I get a final answer of around 37. Destroyer says to take the 4th root of both sides and then cube both sides to cancel out the 4/3 and then you get a final answer of 5. Why did they do the opposite?

Thank you in advance

 

[allyphoe]

Because you're not performing the same operations both times. You want to get rid of an exponent of 4/3, so you need to take the 4th root, then cube the result, or cube both sides then take the 4th root of the result. In both cases, you're applying an exponent of 3/4.

When you arrived at ~37, you applied a second exponent of 4/3.

 

[pasteriori]

(a+3)^4/3 = 16

(a+3)^1/3 = 4rth root of 16 = 2

(a+3) = 2^3 = 8

a = 8 - 3 = 5

anyone can double check?

 

[DAT Destroyer]

I am getting confused with the concepts of fractional exponents. For example lets say I have 27^(4/3). I know you take the cube root and then do the 4th power or 4th power and then cube root it and you get the same answer. Here is where I am getting confused. A question on math destroyer asks to find the value of a. The problem is (a+3)^(4/3) = 16. However, if I cube root both sides and then do the 4th power to both sides to cancel the 4/3 out, I get a final answer of around 37. Destroyer says to take the 4th root of both sides and then cube both sides to cancel out the 4/3 and then you get a final answer of 5. Why did they do the opposite?

Thank you in advance

Since we are looking for a we need to get rid of the (4/3) so we rise both sides to the power of (3/4). And you get:
(a+3)=16^(3/4) = 16^(1/4)^3 =2^3 = 8

And this gives us a = 5

Hope this helps.