Anumber to the 11th power divided by the same number to the 8th power equals 64. what is the number

The number for the given statement is 4

Step-by-step explanation:

Given as :

The statement is written as

A number to the 11th power divided by the same number to the 8th power equals 64.

Let the number = n

So, As per statement

= 64

Now, from the indices method

I.e if the base of the indices are same then the power are subtracted

So, Here the base is n   and  the power is 11 , 8

So, this can be written as

= 64

Or, n³ = 64

I.e n = ∛64

So, The cube root of 64 is 4

So, number = n = 4

Hence The number for the given statement is 4   Answer

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places