Question

Please Simplify:

(root5 a^7/2)^4 a^3/a^8

So confused, I tried figuring this out but need some help tracing the steps. I would appreciate some feedback! Thanks!

Answer 1

I have assumed that the fraction 7/2 is enclosed in parentheses, as follows:

(sqrt(5)*a^(7/2))⁴ a³/a⁸

Since the bases of the exponents are "a" or 5, you only have to apply the following rules of exponents to get your answer of 25a⁹.

1. sqrt(5) = 5^1/2
2. distributive law:
(ab)^x = a^x b^x
3. addition of exponents of same base
a^x a^y = a^x+y
4. multiplication of exponents
(a^x )^y = a^xy

So:
(sqrt(5)*a^(7/2))⁴ a³/a⁸
=(sqrt(5)⁴*(a^(7/2))⁴) a^3-8
=25 a¹⁴ a^-5
=25 a⁹

Answer 2

WOW Thanks for the reply, but I still do not get how we get 25a^9. Can you please further explain. Thanks!

Answer 3

I get 25a^9/16? How can this be? Please help, still confused, thanks!

Answer 4

If you show your steps, it may help me spot where it has gone wrong.

Answer 5

...
=(sqrt(5)⁴*(a^(7/2))⁴) a^3-8
=5^(1/2)*4*a^(7/2)*4*a^3-8
=25 a¹⁴ a^-5
=25 a⁹

the denominator 2 in the fraction (7/2) is an exponent and not a simple number. This is probably from where you got the 16.