Question

I need help SHOW YOUR WORK

Answer 1

Answer:

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

Step-by-step 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:

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

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