Question

Bob has three pennies. Betty has three times as many pennies as Bob. Bill has three times as many pennies as Betty. Barb has three times as many pennies as Bill. How do you express the number of pennies Barb has in exponential form?

Answer 1

Barb has `3^4` pennies

Explanation:

`color(white)("xxxxxxxxxxxxxxxxxx)`Barb: `3^4`
`color(white)("xxxxxxxxxxxxxxxxxxxx")uarr`
`color(white)("xxxxxxxxxxxxx)`Bill: `3^3`
`color(white)("xxxxxxxxxxxxxx")uarr`
`color(white)("xxxxxxx)`Betty: `3^2`
`color(white)("xxxxxxx")uarr`
`color(white)("xx)`Bob: `3^1`

Answer 2

`3^4` pennies, or `81` pennies

Explanation:

Let the number of pennies Bob has equal `x`
Therefore, `x=3`, but we will make the substitution later.

Betty has three times as many pennies as Bob, so she has `3x` pennies.

Bill has three times as many pennies as Betty, so he has `3*3x = 3^(1+1)x = 3^2x` pennies.

Barb has three times as many pennies as Bill, so she has `3*3^2x = 3^(1+2)x = 3^3x` pennies.

Substituting `x` for `3`, Barb has `3^3 * 3 = 3^(1+3) = 3^4` pennies, which is `3times3times3times3 = 81` pennies.