Solving Exponential Power Function

Introduction of solving exponential power function:-
Before solving the exponential power function, students does study about the exponential function definition, formulas and also solve the example problems. In mathematics exponential means ex, where e is the significance of ex the same value again consequent.
For example,
`4e^x` is an exponential function
It is more helpful for exam preparation and also improve our own practice skills.

Basic Properties of Solving Exponential Power Function:-

In the following basic properties of solving exponential power function

`e^x e^y = e^(x+y)`
`(e^x)^p = e^(px)`
`(de)^x/dx = e^x`
`(de^ax)/dx = ae^ax`
`d^n e^ax/dx^n = a^n e^(ax)`
`e^x/e^y = e^(x-y)`

Example Problems for Solving Exponential Power Function:-

Problem 1:-

Solving multiplying the exponential expressions `(-2mn^7 p^2)^4`

Solution:

Given: `(-2mn^7 p^2)^4`

Take all the common terms

= `(-2)^4 m^4 (n^7)^4 (p^2)^4`

= `16 m^4 n^28 p^8`

Multiply the both left side values and get 16 then multiply the power values.

Finally we get an answer as `(-2mn^7 p^2)^4 = 16 m^4 n^28 p^8`


Problem 2:-

Solving add the exponential expressions `x^(3) +x^(4)`

Solution:

Given: `x^(3) +x^(4)`

Take the common term x.

= `x^(3+4)`

= `x^(7)`

Adding the both values and get 7.

Finally we get an answer as `x^(3) +x^(4) = x^(7)`


Problem 3:-

Find an exponential power function `f(x) = x^2 x^5`

Solution:-

Given: `f(x) = x^2 x^5`

We know the formula `e^a e^b = e^(a+b)`

`f(x) = x^2 x^5`

`= x^(2+5)`

`f(x) = x^7`

We get a answer as `f(x) = x^2 x^5`

`= x^7`

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Problem 4:-

Check whether the point (0, 1) lies on the graph of the function y = 4(7)x.

Solution:-

Substitute x = 0 in the function y = 4(7)x.

y = 4(7)0

= 4(1)

= 4

The y–coordinate of the point is 1, which does not match with the obtained value y = 4.

So, the graph of the function y = 4(7)x does not contain the point (0, 1).