Question

I'm trying to solve the expression in the picture shown above, could someone explain how to solve this, step by step?

I'm new to this so please, show your work! :) thank you in advance

Answer 1

this is like a function, all you need is to replace X with the identified X

1/4 × (2)^5

= 32/4

=8

Answer 2

8

Explanation:

Given expression:

`(1)/(4)(2)^x`

To evaluate the given expression for x = 5, begin by substituting x = 5 into the expression:

`(1)/(4)(2)^5`

In mathematics, an exponent tells us how many times a base number is multiplied by itself. In this case, 2 is the base, and 5 is the exponent. This means that we need to multiply 2 by itself 5 times:

`2 * 2 * 2 * 2 * 2=32`

Therefore, as 2⁵ = 32, the expression becomes:

`(1)/(4)(32)`

In mathematical notation, when a number or a variable is placed adjacent to parentheses, it implies multiplication. So, we now need to multiply 1/4 by 32. When multiplying a fraction by a whole number, we multiply the numerator of the fraction by the whole number, and the denominator remains unchanged:

`(1)/(4) * 32 = (1 * 32)/(4)=(32)/(4)`

Finally, simplify the fraction by dividing both the numerator and the denominator by their greatest common factor. In the case of 32/4, the greatest common factor is 4, so we divide the numerator and denominator by 4:

`(32/ 4)/(4/ 4)=(8)/(1)`

Remember that any number divided by 1 is equal to the number itself. So, the final evaluation of the given expression when x = 5 is 8:

`(1)/(4)(2)^5=\boxed{8}`