Question

find the value of 1/81=3power'c'

Answer 1

$\textbf{\huge{ANSWER:}}$

$\sf{Question:}$

Find the value of $\frac{1}{81} = 3^{c}$

$\sf{Solution:}$

Let's simplify 81 first.

81 = $9^{2}$

Now that we have the simplified value of 81, and we know that:

9 = $3^{2}$

We can easily put the value of 81 as:

81 = $3^{4}$

And the rule of exponents says that:

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

Therefore, $\frac{1}{3^{4}}$ :

$\tt{3^{-4}}$

Now, we have :

$3^{-4} = 3^{c}$

Taking only the powers, we get:

=》 $\tt{\huge{c = (-4)}}$

We've just used the rules of exponents which are taught before. Use the comments section to ask your doubts!

Answer 2

Find the value of 1/81= 3^c.

Step by step explanation :

$\frac{1}{81} = 3 {}^{c}$

Now, Simplifying the denominator 81 ( Expanding form ), we get :

$\frac{1}{9 \times 9}= 3{}^{c}$

Now,

Expand the denominator of L.H.S more,

$\frac{1}{3 \times 3\times 3 \times 3}=3{}^{c}$

Here, We can write the denominator of L H S as,

$\frac{1}{3{}^{4}}=3{}^{c}$

Thus,

Using the identity,

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

Here,

m = 4

Hence, c = -4

Thus, Value of c is -4.

While Solving such questions, Keep the R.H.S terms as it is.

Just put the value which you get and hence, you will get the answer.

The answer of your question is -4.