Question

(4/9)^(-1/2) ...the answer I am finding isn't correct according to the calculator. Let me show my steps, any help explaining this?

Answer 1

The answer should be 3/2. The calculator is probably going to display the answer as 1.5. When you raise a fraction to a negative exponent, youj will get the same answer if you take the reciprocal of the fraction and change the exponent from a negative, to a positive. Try it and see.

Answer 2

(4/9)^(-1/2)
= (1/4^(1/2))/(1/9^(1/2))
\[\frac{ \sqrt{4} }{ \sqrt{9}}\]
=2/3
but the calc says 3/2

Answer 3

I'm just confused as to where I flip the fraction

Answer 4

Actually, you can read this problem as follows:

\[\left( \frac{ 4 }{ 9 } \right)^{-1/2}=\left( \frac{ 9 }{ 4 } \right)^{1/2}=\frac{ \sqrt{9} }{ \sqrt{4} }=\frac{ 3 }{ 2 }\]

Answer 5

You flip it at the beginning. You can also work it as you did, but when you divide 1 over the quare root of 4 by 1 over the square root of 9, you end up multiplying 1 over the square root of 4 by the reciprocal of 1 over the square root of 9, which is the square root of 9 over 1.

Answer 6

square*

Answer 7

And when you multiply 1 over the square root of 4 by square root of 9 over 1, you get \[\frac{ 1 }{ \sqrt{4} }\times \frac{ \sqrt{9} }{ 1 }=\frac{ \sqrt{9} }{ \sqrt{4} }=\frac{ 3 }{ 2 }\]

Answer 8

Ok, I see. Thank you very much!

Answer 9

You are most welcome.