Question

Simplify the following using the laws of exponents:

Need help with these:

a) (9)^1/2 x 4^2/24

b) 16 x 2^x+2

Simplify each of the following:


b) b) 3 sqrt x^1/4 sqrt x/ 5 sqrt x^2

c) (ab)^2x+y /a^x b^y

Need these answers double checked:

c) 3^-8/3^-6 x 3^-5
3^-8/3^-6+-5
3-8^ 3^-11
3^-19

d) (4^-2 x 2^-4)^-1
(4^2 x 2^4)
4^2 2^4

Answer 1

a) (9)^1/2 x 4^2/24
according to the way you typed it...
= 3 x 16/24
= 2

b) you probably meant
16 x 2^(x+2)
= 2^4 x 2^(x+2) = 2^(x+6)

3 sqrt x^1/4 sqrt x/ 5 sqrt x^2
- the order of operation is too ambiguous , use brackets to make it clear.

c) 3^-8/3^-6 x 3^-5
= (3^-8)/(3^-6) * (3^-5)
= 3^(-8 + 6 - 5)
= 3^-7
or
1/3^7

(4^-2 x 2^-4)^-1
= 4^2 * 2^4
= 16(16) = 256

notice we use * or brackets for multiplication and
we use / for ÷