Question

Find the value of ( 5)-² ÷ (5)⁴​

Answer 1

Given,

$\frac{(5)^{-2} }{(5)^{4} }$

We have to find the value of given expression

Here, the numerator is in the form of $a^{-m}$

Formula,

$a^{-m} = \frac{1}{a^{m} }$

Here,

$a= 5$

$m = 2$

Now, substitute the above values in the formula, we get

$5^{-2} = \frac{1}{5^{2} }$

According to question,

$\frac{(5)^{-2} }{(5)^{4} }$

We can written as

$\frac{1}{5^{2}\times 5^{4} }$

Here, the denominator is in the form of $a^{m}\times a^{n}$

Formula,

$a^{m}\times a^{n}= a^{m+n}$

Here,

$a=5$, $m=2,n=4$

Now, substitute the values in the above formula,

$=\frac{1}{5^{2}\times 5^{4}}$

$= \frac{1}{5^{2+4} }$

$= \frac{1}{5^{6} }$

$= 5^{-6}$

Therefore, the value of $\frac{(5)^{-2} }{(5)^{4} }$ if $5^{-6}$.

Answer 2

As per the data given in the question,

We have to find the value of given expression,

As from the question,

It is given that,

$\frac{(5)^{-2} }{(5)^{4} }$

 Here, the numerator is in the form of $a^{-m}$

As we know that,

$a^{-m} = \frac{1}{a^{m} }$

Here,

a= 5

m = 2

Now, substitute the above values in the formula, we will get

$5^{-2} = \frac{1}{5^{2} }$

So, we will get,

$\frac{(5)^{-2} }{(5)^{4} }$

We can written as

$\frac{1}{5^{2}\times 5^{4} }$

Here, the denominator is in the form of $a^{m}\times a^{n}$

So, for simplying the given expression,

We will use the identity,

$a^{m}\times a^{n}= a^{m+n}$

Here,

a=5, m=2,n=4

Now, substitute the values in the above formula,

$=\frac{1}{5^{2}\times 5^{4}}\\= \frac{1}{5^{2+4} }\\= \frac{1}{5^{6} }\\= 5^{-6}$

Therefore, the value of $\frac{(5)^{-2} }{(5)^{4} } \:is\: 5^{-6}.$