Can you please help me simplify these expressions?(only 2 problems)?

Question

1. (3/2)^-3
2. (4/5)^-2
Thanks in advance.

Answer 1

It's been a while since I've done this kind of thing, but I'll take a crack at it anyways, borrowing some laws i picked up off of other peoples answers, but they are the right ones so it shouldn't matter one way or the other.
Ok, (3/2) to the negative 3rd power, is the same as 1/(3/2 to the 3rd power). So first things first, (3/2) * (3/2) * (3/2) = (27/8), and 1/(27/8), is the same as it's reciprocal of (27/8), or (8/27), so the answer to 1 is:
1.) (8/27), which can't be simplified, so that's your answer as far as I can tell.

Now number 2, (4/5) to the negative 2nd power is the same as 1/(4/5 to the 2nd power), or, (4/5) * (4/5) = (16/25), so rewritten it's, 1/(16/25), to simplify further find the reciprocal of (16/25), or (25/16), so your answer to the second problem is:
2.) (25/16)

Hope you understand how that works, (assuming I did it right),
and I hope that helps you.

Answer 2

Be careful...some of the others are WRONG (3^3 is NOT 9...it's 27 !)

Anyway, here is the solution;

(3/2)^-3 is the same as 1/(3/2)^3 >>> this becomes 1/{(3/2)(3/2)(3/2)} >>> which is 1/(27/8) >>> remember how if you have a fraction as the denominator of a fraction, you "invert" and multiply ? So, it becomes 1/1 times 8/27 = 8/27. This can't be simplified any more, but if you solve it in decimal form, it is 0.296.

The second one is the same way; 1/(4/5)^2 >>> 1/{(4/5)(4/5)} >>> 1/(16/25) >>> 16/25 >>> 0.64

Hope this helps...good luck !

Answer 3

All you need to do is deal with the fraction in pieces

For example, (3/2)^3
First cube 3 = 27
Then cube 2 = 8
The answer is 27/8

(4/5)^2
4^2= 16
5^2 = 25
therefore, (4/5)^2 = 16/25

hope that helps!


oh and also, reading everyone else's answers... no one is cubing the 3 in the first problem, they're only cubing the 2...
3^3 = 3 times 3 times 3 = 27!!! not 9!!!!

Answer 4

(3/2)^-3 = 1/(3/2)^3 = 1/(3/2 * 3/2 * 3/2) = 1/(9/8) = 8/9

(4/5)^-2 = 1/(4/5)^2 = 1/(4/5 * 4/5) = 1/(16/25) = 25/16 = 1 9/16

Hope this helps! :)

Answer 5

Here are some important hints for you to solve the problems yourself.
(Note: None of the above got both answers correct)

x ^ -y = 1 / (x ^ y)

and

(3/2) ^ 3 = (3/2) * (3/2) * (3/2) = 27/8

and

1 / ( a / b ) = b / a

Answer 6

3^-3/2^-3
3 times three is nine
so -9
2 times 2 is four, four times two is 8
s0 -8
-9/-8

4^-2/5^-2
4 times 4 is 16
so -16
5 times 5 is 25
so -25
-16/-25

Answer 7

1. 27/8
2. 16/25