Question

The value of 30 is. (a) 0 (b) 3

(c) 1

(d) None of these

Answer 1

$\displaystyle \sf{ The \: value \: of \: \: {30}^{0} \: is \bf \: 1}$ [ The correct option is (c) 1 ]

Correct question :

$\displaystyle \sf{ The \: value \: of \: \: {30}^{0} \: is }$

(a) 0 (b) 3 (c) 1 (d) None of these

Given :

$\displaystyle \sf{ {30}^{0} }$

To find :

$\displaystyle \sf{ The \: value \: of \: \: {30}^{0} \: is }$

(a) 0

(b) 3

(c) 1

(d) None of these

Concept :

We are aware of the formula on indices that

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

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is $\displaystyle \sf{ {30}^{0} }$

Step 2 of 2 :

$\displaystyle \sf{ Find \: value \: of \: \: {30}^{0} }$

We are aware of the formula on indices that

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

Now take a = 30 , n = 0

So we get from above

$\sf{ {30}^{m} \times {30}^{0} = {30}^{m + 0} }$

$\sf{ \implies {30}^{m} \times {30}^{0} = {30}^{m } }$

$\sf{Dividing \: both \: sides \: by \: \: {30}^{m} \: \: we \: get }$

$\sf{ \implies {30}^{0} = \dfrac{{30}^{m}}{{30}^{m}} }$

$\sf{ \implies {30}^{0} = 1 }$

$\displaystyle \sf{ \therefore The \: value \: of \: \: {30}^{0} \: is \bf \: 1}$

Hence the correct option is (c) 1

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