twentyfive to the power of -2/3?

Question

mathematics sum,25^-2/3

Answer 1

25^ -2/3

= 1/(25^2/3)

=1/cube root of 25^2

=1/ cube root of 625

= 1/ 5(cube root of 5)

Answer 2

Everybody's giving you answers, but nobody explained how... or why... they got them.

There are a couple of rules... well, four actually... regarding exponents that are applicable here, and with which you should be familiar.
1. (a^p)(a^q)=a^(p+q)
2. (a^p)^q=a^(pq)
3. a^0-1
4. a^1=a

The problem you have posed is
25^(-2/3)
Um... that carat symbol, "^" means that the term to the left is being raised to the power of the term to the right. For example a^2 means a squared.

Think about rules 1 and 3 above fir a moment,'
-2/3+2/3=0, Right?
Ok, so [25^(-2/3)] [25^(2/3)] = 25^0 = 1
That menas that [25^(-2/3)] is the reciprocal of [25^(2/3)] sometimes written as 1/[25^(2/3)]
That's why they're writing it that way,.

The 2/3 part might look a little confusing. What's that 1/3 thing?
Ok, consider rules 2 and 4 above.
2/3 = (2)(1/3), Right?
Using the second rule, that makes the problem
[25^(-2)]^(1/3)

We've already established that 25^(-2) can be written as 1/(25^2)=1/625... but there's that 1/3...

Look at rule 2.
You know that (3)(1/3)=1, right?
And you know what raising something to the 3rd power (a^3) means, right?
Ok applying the second rule (a^3)^(1/3) = a^1 = a
That makes a^(1/3) what is called in some circles, "the curb root" of a. That kind of makes sense. If you cube a number and take the cube root of that result, you should get the number back.

So, what the problem is asking you to do is to take the cube root of the reciprocal of the square of 25..

Now you know what it's all about, you can figure it out for yourself so you can figure out which of the answers is correct.

Answer 3

25^(-2/3) means: "the cube root of 25², then take the reciprocal"

so you have the cube root of 5*5*5*5, which is 5* ³√5. When you take the reciprocal, you have:

1/(5* ³√5)

In order to rationalize a fraction that has a cube root in its denominator, you must multiply the top and bottom by whatever cube root would make a perfect cube. This would be ³√25. So you would have:

[1/((5* ³√5)] * [³√25/³√25]
= ³√25 / (5* ³√125)
= ³√25 / 25

What's with all you people just plugging it into a calculator? My 7 year old nephew could do that!

Answer 4

1 / (3√(25^2))

Written: The reciprocal of the cube root of 25 squared.

It's 0.1169607095.

Answer 5

when you have a fraction for a power...think power over root.

when you raise something to the 1/3 power...you are actually taking the cube root of that number...

in this problem you are raising 25 to a -2/3 power

1/[³√(25)²] = 1/[5 * ³√5]

i don't have a calcualtor...but you could plug that in and you should get ur answer!

Answer 6

the three on the backside means cube root, so cube root of 8 is two. the two on suitable mean squared, so sq. the two to get 4. The minus sign means a million over, so do a million over 4 to get a million/4. Melissa, it truly isn't difficult for GCSE, they're on the specification.

Answer 7

25^-2/3
=1/25^2/3
=1/³√25²
=0.1169

Answer 8

0.12 (to 2 sig figs)

Answer 9

0.11696