Square Root/Exponents Problem Help?

Question

I appreciate it if I can get help solving the following problem.

What is (x^8)^1/2?

Answer 1

With exponents in this fashion, you multiply the exponents together. The answer would therefore be

x^(8*0.5)

=x^4

Answer 2

=x^8/2=x^4

Answer 3

(x^8)^1/2 will be X^8*1/2 which is x^4

Answer 4

Okay, so I will help you understand the concept and hopefully you will be able to answer this question and probably the many others you will have on homework and tests.  An exponent, as I am sure you know, means to multiple that integer or variable by itself that specific number of times.  

1.Lets use (x^3)^3 for example:

So the first exponent is three meaning (x*x*x)^3

2.Now take the outside exponent, you will have

(x*x*x) * (x*x*x) * (x*x*x)

3. If you look at the problem now, you should be able to tell the parentheses are not needed and you really have x multiplied by itself 9 times.  These means that (x^3)^3 = x^9.

4. The following result is the exponent rule:

(x^m)^n = X^(m*n) , in this case where m and n are real numbers.

So lets do (x^m)^1/2:

The result is x^(m*1/2) or x^(m/2).

Hope this helps!

Answer 5

x^4

(Remember when you have two exponents on top of each other like that, you can combine them by multiplying them, simplifying the problem.  Review those rules in your math text.)