Question

A student said that
$\frac{{3}^{5} }{{9}^{5} }$
is the same as
$\frac{1}{3}$
What mistake has he made?
​

Answer 1

Answer:

Students mistook 3^5 / 9^5 as ( 3 x 5 ) / ( 9 x 5 ).

Step-by-step explanation:

= > ( 3^5 ) / ( 9^5 )

= > ( 3^5 ) / { ( 3^2 )^5 }

= > ( 3^5 ) / { 3^(10) }

= > 3^( - 5 )

So it can be clearly said that the student made a mistake.

= > 1 / 3

= > ( 3 / 9 )

= > { 3 x 5 } / { 9 x 5 }

From this, we can say that students might have assumed 'power of 3 and 9' as 'numbers multiplied by 3 and 9'.

It means : Students mistook 3^5 / 9^5 as ( 3 x 5 ) / ( 9 x 5 ).

This could be the reason.

Answer 2

Answer:

$\bold{Solution:-}$

The student took $\bold{\dfrac{{3}^{5} }{{9}^{5} } }$ as $\bold{\dfrac{1}{3} }$

What he made mistake can be found out by 1 method.

$\bold{Method:-}$

He would have taken $\bold{\dfrac{{3}^{5} }{{9}^{5} }}$ as $\bold{\dfrac{3\times 5}{9 \times 5}}$

$\Rightarrow\sf \dfrac{{3}^{5}}{{9}^{5}} \\\\\Rightarrow\sf \cancel{\dfrac{243}{59049}} \\\\\Rightarrow\sf \dfrac{1}{243} \neq \dfrac{1}{3}$

$\therefore$ He has surely made a mistake in this.

Because, $\Rightarrow\sf \dfrac{3\times 5}{9 \times 5 } \\\\\Rightarrow\sf \cancel{\dfrac{15}{45}} \\\\\Rightarrow\sf \dfrac{1}{3} = Taken\:solution$

$\rule{300}{1}$

So, the student mistook powers of 3 and 9 as multiplier of 3 and 9.

As a result, the equation becomes wrong as a fact.