Need help with Exponents & Square Roots!?

Question

Hi everyone - trying to solve the square root of x with the index of 5 (multiplied by)* the square root of x. The book's answer is x ^7/10 ( ^ to the power of) but I am not seeing where they get 7/10's at! Can anyone lend some insight? Thank you!

Answer 1

root x with index 5 means x^(1/5)
square root x can be x^(1/2)

If we multiply with the same base, then we add exponents
(recall x^a * x^b = x^(a+b)

x^(1/5) * x^(1/2) = x^(1/5+1/2)

find LCD to add 1/5 + 1/2 = 2/10 + 5/10 = 7/10

ANSWER x^(7/10)

=]

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Answer 2

"square root of x with the index of 5" is pronounced "the fifth root of x," and equals x^(1/5). Of course, the square root of x equals x^(1/2).

Laws of Exponents -----> x^a * x^b = x^(a + b):

x^(1/5) * x^(1/2)

= x^(1/5 + 1/2)

= x^(7/10)

* I'm a Level 5. I have just finished integral calculus. Why do you ask?

Answer 3

(x^1)^(1/5) * x^(1/2)

=x^(1/5+1/2)
=x^(7/10)

Answer 4

convert the radicals into rational powers:
x^(1/5)*x^(1/2)=x^(1/5+1/2)=x^(2/10+5/10)=x^(7/10)

Answer 5

well ask ur teacher because he/she is the one that should teach u