anyone up to a MATH equation?

Question

HOW do you simplify this:
(81a to the power of 10) to the power of 1/2

and the exact value of:
(2 to the power of 1/4) to the power of 1/2

please explain
(its easier to write it out since i can't type in the indicies)

Answer 1

Question 1
[ 81 a ^(10) ]^(1/2)
= 9 a ^ 5

Question 2
[ 2^(1/4) ]^(1/2)
= 2^(1/8)

Answer 2

(81a^10)^(1/2) = √81a^10 = 9a^5

(2^(1/4))^(1/2) = 2^(1/8) = the 8th root of 2. This exact value is found by taking the square root of 2, then the square root of this answer, then the square root of this next answer. So √2 = 1.4142135. Then √1.4142135 = 1.189207. Finally √1.189207 = 1.0905076. This works because (1/2)^3 = 1/8.
This was done on a small $2.00 calculator. Or type in 2^(1/8) on a better calculator for the answer faster.

Answer 3

(81 a^10) ^ 1/2 = (81)^(1/2) * (a^10)^(1/2) = 9 a^5

(2 ^ 1/4) ^ 1/2 = 2 ^ 1/8 (the eighth root of two)

I can't give you an exact value for it; it's irrational.

Answer 4

(x to the power of a)to the power of b = x to the power a*b
in your case
is 81ato the power of 5
and 2 to the power of 1/8

Answer 5

(81a)^(10)^(1/2)=(81a)^(5)
(2^(1/4) to the power 1/2
=2^(1/8)=1.0905 (calculator or computer)

2^3=2x2x2=8
(2^3)^3=(2^3)(2^3)(2^3)=(2x2x2)(2x2x2)(2x2x2)=2^9
(a^b)^c=a^bc

Answer 6

when you have
a to the pwoer of b to the power of c
you just multiply both powers

ie a to power bc

Answer 7

1) 3.48678 * 10^9 a

2) 1.09051

keep in mind of sig. digs!

Answer 8

1) 3.48678 * 10^9 a

2) 1.09051 (to 5 dp)

The first is easy its, (81a^10)^1/2

The 2nd is also simple.....(2^1.4)^1/2