Question

N the numerical sentence below, A = 8, D =1/2 , and F =1/4 . What are the values B, C, and E if the sentence below is equivalent to the numerical sentence, 2 × 4 = 8?

Answer 1

`B = (1)/(3)`

`C = 16`

`E = 4096`

Explanation:

Given

`A^B * C^D = E^F` --- Missing from the question

`2*4 = 8`

`A = 8`

`D = (1)/(2)`

`F = (1)/(4)`

Required: Find B, C and E

Substitute values for A, D and F in
`A^B * C^D = E^F`

`8^B * C^{(1)/(2)} = E^{(1)/(4)}`

Compare the above expression to:
`2*4 = 8`

We have:

`8^B = 2`

`C^{(1)/(2)} = 4`

`E^{(1)/(4)} = 8`

In
`8^B = 2`

Express 8 as a 2^3

`2^(3B )= 2^1`

Cancel out 2

`3B = 1`

`B = (1)/(3)`

In
`C^{(1)/(2)} = 4`

Express 4 as
`16^{(1)/(2)}`

`C^{(1)/(2)} = 16^{(1)/(2)}`

The exponents cancel out

`C = 16`

In
`E^{(1)/(4)} = 8`

Express 8 as
`4096^{(1)/(4)}`

`E^{(1)/(4)} = 4096^{(1)/(4)}`

The exponents cancel out

`E = 4096`