Question

Simplify each expression. Assume that all variables are positive.
1) \[(4x ^{-2}y^4)^{-1/2}\]
2) \[(8ab^2)^{-1/2}(8ab^2)^{1/2}\]
3) \[(s ^{2/5}t ^{1/3})(s ^{1/2}t ^{1/2})\]
I really have no idea how to do them. Explain and show steps please!

Answer 1

1. (4x^-2 y^4 )^-1/2
= 1/ [4x^-2 y^-4) ^ (1/2) ]
= (x^2)^(1/2) / [4y^-4) ^ (1/2) ]
= x/(2y^2)

Answer 2

2. (8ab^2)^(-1/2) (8ab^2)^(1/2)
= (8ab^2)^(1/2) / (8ab^2)^(1/2)
=1

Answer 3

well you need to know that x^(-a) = 1/ (x^a)

Answer 4

3.
8^(2/5) t^(1/3) 8^(1/2) t^(1/2)
= 8^ (2/5 + 1/2 ) t^(1/3 + 1/2)
= 2^(3x9/10) t^(5/6)
= 2^(27/10) t^(5/6)

Answer 5

The answer for 2 is just 1?

Answer 6

yes
=(8ab^2)^(-1/2 + 1/2)
= (8ab^2)^(0)
=1
note that a^0 = 1

Answer 7

or @campbell_st @amistre64

Answer 8

when multiplying the rule is add the powers of the same pronumeral

for s its 2/5 + 1/2 = 9/10

for t its 1/3 + 1/2 = 5/6

\[s^{9/10}t^{5/6}\]

Answer 9

so that's all?

Answer 10

yep... index laws... the rule applies for multiplication

Answer 11

@campbell_st are all the other answer good too?

Answer 12

I haven't looked at them... been busy... sorry... I don't have time

Answer 13

@campbell_st it's okay look at them when you have time and let me know please