How do you square root exponents?

Question

For instance, how would you square root a^10?

the question I got is:

(a^10/25b^-4)^1/2 and the answer they gave is (a^5)(b^2)/5 

I understand how they got all of it except a^5. I'm guessing square rooting an exponent is just dividing it by two, but I don't want to assume. if that's the case, would cube rooting an exponent mean dividing it by 3?

Thanks!

MsMath · Accepted Answer

You multiply the exponents by 1/2.

(a^10/(25b^-4))^(1/2)

= (a^10)^(1/2) / [25b^-4]^(1/2)

(a^10*1/2) / [25^(1/2) b^(-4*1/2)]

= a^5/(5b^-2)

= a^5 b^2 / 5

? · Answer

undergo in ideas the Order of Operations: PEMDAS (Please Excuse My expensive Aunt Sally) Parenthesis Exponents Multipication branch Addition Subtraction you often might desire to accomplish the better operation till now something is done. on your case, it may be the sq. root of x^4. when you consider that x^4 is interior it (parenthesis) and is an exponent, it would be achieved first. Then, and in uncomplicated terms then, are you able to take the sq. root, which could be x^2.

3starLUSVIMINDA · Answer

(a^10/25b^-4)^1/2
soln
((a^10b^4)/25)^1/2
{a^(10*1/2)} {b^(4*1/2)} /(25)^1/2
{a^(10/2)} {b^(4/2)} /(5*5)^1/2
ans
{a^(5)} {b^(2)} /(5)

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How do you square root exponents?

3 Answers