Answer:
[tex] F)\displaystyle \: 100\pi{ x}^{8} {y}^{2} {z}^{ 6} [/tex]
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:
[tex] \displaystyle \: S = 4\pi( {5x}^{4} y {z}^{ 3} {)}^{2} [/tex]
recall law of exponent
[tex] \displaystyle \: ({x}^{m} {)}^{n} \iff \: {x}^{mn} [/tex]
to simplify:
[tex] \displaystyle \: S = 4\pi({ {5}^{2} x}^{4 \times 2} {y}^{1 \times 2} {z}^{ 3 \times 2} )[/tex]
simplify multiplication:
[tex] \displaystyle \: S = 4\pi({ 25x}^{8} {y}^{2} {z}^{ 6} )[/tex]
distribute:
[tex] \displaystyle \: S = 100\pi{ x}^{8} {y}^{2} {z}^{ 6} [/tex]
hence our answer is F
