Question

solve for the varaiables shown in the steps simplifiying the expression below: 2^5 × 8^4/16 = 2^5 × (2^a)^4/2^4 = 2^5 × 2^b/2^4 = 2^c

Answer 1

given the expresions

Solving a

`(2^5*8^4)/(16)=(2^5*(2^a)^4)/(2^4)`
`(8^4)/(16)=((2^a)^4)/(2^4)`
`(8^4)/(16)=((2^a)^4)/(16)`
`8^4=(2^a)^4`
`8=(2^a)`
`a=3`

Solving b

`(2^5\cdot8^4)/(16)=(2^5*2^b)/(2^4)`
`(2^5\cdot8^4)/(16)=(2^5*2^b)/(16)`
`2^5\cdot8^4=2^5*2^b`
`8^4=2^b`
`((2)^3)^4=2^b`
`2^(12)=2^b`
`b=12`

solving C

`\:(2^5\cdot8^4)/(16)=2^c`
`\:(2^5\cdot2^(12))/(2^4)=2^c`
`\:(2^((5+12)))/(2^4)=2^c`
`\:(2^((17)))/(2^4)=2^c`
`\:2^((17-4))=2^c`
`\:2^((13))=2^c`
`C=13`

then

A=3

B=12

C=13