Name: Exponential Form of a Number
Uploaded: 2019-07-19
Duration: 3 min 10 s
Description: Every composite number can be expressed as a product of its prime factors. In this video, let us learn to express the number in its exponential form by findi...

Question

If $m = - 2$ and $n = 2$ ; find the value of $m^{n} + n^{m}$ .

Accepted Answer

The notation for writing the product of a number several times is called exponential notation or power notation.

For any rational number $a, a^{m}$ corresponds to number obtained by multiplying the rational number $m^{n} + n^{m}$ for $m$ number of times.

In exponential notation $a^{m}$ , $a$ is called the Base and $m$ is called the exponent, the exponent about how many times the number is going to get multiplied.

For example: $a^{m} = a \times a \times a . . . . . . . . m$ times

In the given question, we have $m^{n} + n^{m}$

$= {(- 2)}^{2} + {(2)}^{- 2}$

Using the laws of exponents, $a^{- m} = \frac{1}{a^{m}}$

$\Rightarrow 4 + \frac{1}{2^{2}}$

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

$\Rightarrow \frac{17}{4} = 4 \frac{1}{4}$

Hence, the value of $m^{n} + n^{m}$ is $4 \frac{1}{4}$ .

If $m = - 2$ and $n = 2$ ; find the value of $m^{n} + n^{m}$ .

Important Questions on Exponents

Learn and Prepare for any exam you want !

If m=-2 and n=2; find the value of mn+nm.

Important Questions on Exponents

Learn and Prepare for any exam you want !

If $m = - 2$ and $n = 2$ ; find the value of $m^{n} + n^{m}$ .