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Sagot :

Nayefx

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

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