Question

Let me ask this again...

Simplify (15/25)^-3

I can only simplify it up to 1/(3/5)^3, which is where I am stuck. Is this as far as it can go, or is there more to it? Please help!

Answer 1

^
This is as far as I can go before I get stuck. Is this the answer or not?

Answer 2

Not quite you are almost there, just look at the denominator first (ignore the numerator). What is (3/5)^3?

Answer 3

That's where I get confused, because I think I might be doing it wrong.

Answer 4

well whats (3/5)*(3/5)*(3/5)?

Answer 5

or alternatively (3*3*3)/(5*5*5)?

Answer 6

simplify the brackets 1st

\[\frac{15}{25} = \frac{3}{5}\]

using index notation it can be written as

\[\frac{3}{5} = 3^1 \times5^{-1}\]

using the power of a power law

\[(x^a)^b = x^{a \times b}\]

the problem is

\[(3^1 \times 5^-1)^{-3} = 3^{1 \times -3} \times 5^{-1\times -3}\]

which gives

\[3^{-3} \times5^3\]

using fraction notation is \[\frac{1}{3^3} \times 5^3 = \frac{5^3}{3^3} = \frac{125}{27}\]

Answer 7

or just read campbell's answer

Answer 8

OK, thanks!