Question

I need help SHOW YOUR WORK

Answer 1

`F)\displaystyle \: 100\pi{ x}^(8) {y}^(2) {z}^( 6)`

Explanation:

we are given r and the formula

we want to find the surface area of the shpare with the given r

to do so

we need our algebra skills

substitute the value of r:

`\displaystyle \: S = 4\pi( {5x}^(4) y {z}^( 3) {)}^(2)`

recall law of exponent

`\displaystyle \: ({x}^(m) {)}^(n) \iff \: {x}^(mn)`

to simplify:

`\displaystyle \: S = 4\pi({ {5}^(2) x}^(4 * 2) {y}^(1 * 2) {z}^( 3 * 2) )`

simplify multiplication:

`\displaystyle \: S = 4\pi({ 25x}^(8) {y}^(2) {z}^( 6) )`

distribute:

`\displaystyle \: S = 100\pi{ x}^(8) {y}^(2) {z}^( 6)`

hence our answer is F