SOLUTION: Simplify A. {{{a^(1/4) * a^(2/5) * a^(-1/10) }}} with the question above my book says the answer is a^(11/20) but i don't understand how this answer has been reached! If

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Simplify A. {{{a^(1/4) * a^(2/5) * a^(-1/10) }}} with the question above my book says the answer is a^(11/20) but i don't understand how this answer has been reached! If      Log On


   

Question 997231: Simplify
A.
a%5E%281%2F4%29+%2A+a%5E%282%2F5%29+%2A+a%5E%28-1%2F10%29+
with the question above my book says the answer is a^(11/20) but i don't understand how this answer has been reached! If you could show the working that would be great!
B. 5sqrt%28a%5E3%2Ab%5E2%29+%2A+5sqrt%28a%5E2%2Ab%5E%28-1%29%29
This one I'm just not sure how to simplify with the square roots so work out would be great once again!
Thank you so so much!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Question #A.
Know the rules for exponents.
In restated rational numbers, because page rendering may be a problem, those exponents are 1%2F4, 2%2F5, and -1%2F10.

a%5E%281%2F4%29%2Aa%5E%282%2F5%29%2Aa%5E%28-1%2F10%29

a%5E%281%2F4%2B2%2F5-1%2F10%29

Continue.....!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify
A.
a%5E%281%2F4%29+%2A+a%5E%282%2F5%29+%2A+a%5E%28-1%2F10%29+
with the question above my book says the answer is a^(11/20) but i don't understand how this answer has been reached! If you could show the working that would be great!
B. 5sqrt%28a%5E3%2Ab%5E2%29+%2A+5sqrt%28a%5E2%2Ab%5E%28-1%29%29
This one I'm just not sure how to simplify with the square roots so work out would be great once again!
Thank you so so much! 
A)     a1/4 + a2/5 - a1/10

         a(1/4 + 2/5 - 1/10) -------- Multiplying expressions with same base, so exponents are added

         a(5/20 + 8/20 - 2/20) ----- Converting fractions to LCD, 20

highlight%28highlight%28highlight%28highlight%28a%5E%2811%2F20%29%29%29%29%29, or a11/20



B).     5sqrt%28a%5E3%2Ab%5E2%29+%2A+5sqrt%28a%5E2%2Ab%5E%28-1%29%29

        5+%2A+5+%2A+sqrt%28a%5E3%2Ab%5E2%29+%2A+sqrt%28a%5E2%2Ab%5E%28-1%29%29

        25+%2A+sqrt%28a%5E3%2Ab%5E2%29+%2A+sqrt%28a%5E2%2Ab%5E%28-1%29%29

        25+%2A+sqrt%28a%5E3%2Ab%5E2+%2A+a%5E2%2Ab%5E%28-1%29%29 --------- Combining RADICANDS into one (1) RADICAL

        25+%2A+sqrt%28a%5E%283+%2B+2%29%2Ab%5E%282+%2B+-+1%29%29

        25+%2A+sqrt%28a%5E5b%29

        25+%2A+sqrt%28a%5E4+%2A+a+%2A+b%29

        25+%2A+sqrt%28%28a%5E2%29%5E2+%2A+a+%2A+b%29, and FINALLY: highlight_green%2825a%5E2+%2A+sqrt%28ab%29%29