Question

Solve for the varaiables shown in the steps simplifying the expression below:

25 ⋅ 84
16
=
25 ⋅ (2a)4
24
=
25 ⋅ 2b

Answer 1

Answer:

a=3

b=12

c=13

Step-by-step explanation:

(see attached)

Answer 2

The value of 'a' is 3, 'b' is 12, and 'c' is 13 and this can be determined by using the arithmetic operations.

Given :

Expression -  $\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}=2^c$

The value of a, b, and c can be determined by following the below calculations:

$\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}$

Further, simplify the above expression:

$\dfrac{2^5\times (2^3)^4}{2^5}=\dfrac{2^5\times (2^a)^{4}}{2^4}$

the above equation holds good when the value of 'a' is 3.

$\dfrac{2^5\times 8^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}$

Further, simplify the above expression:

$\dfrac{2^5\times 2^{12}}{2^5}=\dfrac{2^5\times 2^b}{2^4}$

the above equation holds good when the value of 'b' is 12.

$\dfrac{2^5\times 2^{12}}{2^5}=2^c$

Further, simplify the above expression.

$\dfrac{2^{17}}{2^4}=2^c$

$2^{13}=2^c$

the above equation holds good when the value of 'c' is 13.

For more information, refer to the link given below:

https://brainly.com/question/20595275