Perform the indicated operation. Be sure the answer is reduced.

Question 1

Question 2

$\boxed{ \rm (4x^(2)y^(3)z)/(9) * \frac{45y}{8 {x}^(5) {z}^(5) }}$

$\dashrightarrow \sf(4x^(2)y^(3)z)/(9) * \frac{45y}{8 {x}^(5) {z}^(3) }$

$\\ \\$

$\dashrightarrow \sf( \cancel4x^(2)y^(3)z)/(9) * \frac{45y}{ \cancel8 {x}^(5) {z}^(3) }$

$\\ \\$

$\dashrightarrow \sf(x^(2)y^(3)z)/(9) * \frac{45y}{2{x}^(5) {z}^(3) }$

$\\ \\$

$\dashrightarrow \sf(x^(2)y^(3)z)/( \cancel9) * \frac{ \cancel{45}y}{2{x}^(5) {z}^(3) }$

$\\ \\$

$\dashrightarrow \sf(x^(2)y^(3)z)/(1) * \frac{5y}{2{x}^(5) {z}^(3) }$

$\\ \\$

$\dashrightarrow \sf(x^(0)y^(3)z)/(1) * \frac{5y}{2{x}^(5 - 2) {z}^(3) }$

$\\ \\$

$\dashrightarrow \sf(y^(3)z)/(1) * \frac{5y}{2{x}^(3) {z}^(3) }$

$\\ \\$

$\dashrightarrow \sf\frac{y^(3)z {}^(0) }{1} * \frac{5y}{2{x}^(3) {z}^(3 - 1) }$

$\\ \\$

$\dashrightarrow \sf(y^(3))/(1) * \frac{5y}{2{x}^(3) {z}^(2) }$

$\\ \\$

$\dashrightarrow \sf \frac{5y * {y}^(3) }{2{x}^(3) {z}^(2) }$

$\\ \\$

$\dashrightarrow \sf \frac{5y {}^(0) * {y}^(3 + 1) }{2{x}^(3) {z}^(2) }$

$\\ \\$

$\dashrightarrow \sf \frac{5 * {y}^(4) }{2{x}^(3) {z}^(2) }$

$\\ \\$

$\dashrightarrow \bf \frac{5 {y}^(4) }{2{x}^(3) {z}^(2) }$

$\\ \\$

$\therefore \underline{ \textbf{ \textsf{option \red c \: is \: correct}}}$

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