Question

Question 97:

What's the error?
A student said that $\frac{3^5}{9^5}$ is the same as $\frac{1}{3}$. What mistake has the student made?

Answer 1

We have,
$\frac{3^5}{9^5}=\frac{3^5}{(3^2{)}^5}[\because 9=3\times 3=3^2]=\frac{3^5}{3^{10}}=\frac{1}{3^{10-5}}=\frac{1}{3^5}[\because \frac{a^m}{a^n}=a^{m-n}]So,\frac{1}{3}isnotsameas\frac{1}{3^5}.$
Student has not multiplied the base by its exponent.
This is the error.