# What is the value of the given expression?

I recently got this question in exam. This seems like a very basic question. But since I made it wrong , It might be my basics are not strong.

I solved it this way.

1/1 / 25/1

1*1/1*25

1/25

How ?Can somebody explain.

-
An expression like $a/b/c/d$ is ambiguous. It could mean $(a/b)/(c/d)$, or $a/(b/(c/d))$, or a few other things. It would be a good idea to put in a few parentheses so what you write is not ambiguous. The original question is ambiguous, for similar reasons. Is it $(1/1)/(1/5^{-2})$? $1/(1/(1/5^{-2}))$? – Gerry Myerson Sep 15 '13 at 10:36
If this is the picture from your exam then I think you are right because of the length of the central line and since $$\frac{\frac 11}{\frac 1{5^{-2}}}=\frac 11 \frac {5^{-2}}1=5^{-2}$$ – Raymond Manzoni Sep 15 '13 at 10:37

Denote $\frac{1}{x}$ by $x^{-1}$. By basic property of the exponential, if $n, m \in \mathbb{Z}$, then $(x^{m})^{n} = x^{mn}$.
Your expression above is $(((5^{-2})^{-1})^{-1})^{-1} = 5^{(-2)(-1)(-1)(-1)} = 5^2 = 25$.
The answer is $25$ if the parenthesis is $(1 / (1 / (1/ 5^{-2})))$. Taking a more careful look at the picture, it seems that it could be interpreted as $(1/1)/(1/5^{-2}) = 1 / 25$. I think the picture may be ambiguous. – William Sep 15 '13 at 10:42
If we assume the OP wrote the division lines properly, the expression is $\,\frac{\frac11}{\frac1{5^{-2}}}=5^{-2}=\frac1{25}\;$ and the OP's right. – DonAntonio Sep 15 '13 at 11:31