<h3>Given Equation:-</h3>
![\boxed{ \rm \frac{4x^{2}y^{3}z}{9} \times \frac{45y}{8 {x}^{5} {z}^{5} }}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Crm%20%20%5Cfrac%7B4x%5E%7B2%7Dy%5E%7B3%7Dz%7D%7B9%7D%20%5Ctimes%20%20%5Cfrac%7B45y%7D%7B8%20%7Bx%7D%5E%7B5%7D%20%7Bz%7D%5E%7B5%7D%20%7D%7D)
<h3>Step by step expansion:</h3>
![\dashrightarrow \sf\dfrac{4x^{2}y^{3}z}{9} \times \dfrac{45y}{8 {x}^{5} {z}^{3} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7B4x%5E%7B2%7Dy%5E%7B3%7Dz%7D%7B9%7D%20%5Ctimes%20%20%5Cdfrac%7B45y%7D%7B8%20%7Bx%7D%5E%7B5%7D%20%7Bz%7D%5E%7B3%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{ \cancel4x^{2}y^{3}z}{9} \times \dfrac{45y}{ \cancel8 {x}^{5} {z}^{3} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7B%20%5Ccancel4x%5E%7B2%7Dy%5E%7B3%7Dz%7D%7B9%7D%20%5Ctimes%20%20%5Cdfrac%7B45y%7D%7B%20%5Ccancel8%20%7Bx%7D%5E%7B5%7D%20%7Bz%7D%5E%7B3%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{9} \times \dfrac{45y}{2{x}^{5} {z}^{3} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7Bx%5E%7B2%7Dy%5E%7B3%7Dz%7D%7B9%7D%20%5Ctimes%20%20%5Cdfrac%7B45y%7D%7B2%7Bx%7D%5E%7B5%7D%20%7Bz%7D%5E%7B3%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{ \cancel9} \times \dfrac{ \cancel{45}y}{2{x}^{5} {z}^{3} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7Bx%5E%7B2%7Dy%5E%7B3%7Dz%7D%7B%20%5Ccancel9%7D%20%5Ctimes%20%20%5Cdfrac%7B%20%5Ccancel%7B45%7Dy%7D%7B2%7Bx%7D%5E%7B5%7D%20%7Bz%7D%5E%7B3%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{1} \times \dfrac{5y}{2{x}^{5} {z}^{3} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7Bx%5E%7B2%7Dy%5E%7B3%7Dz%7D%7B1%7D%20%5Ctimes%20%20%5Cdfrac%7B5y%7D%7B2%7Bx%7D%5E%7B5%7D%20%7Bz%7D%5E%7B3%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{x^{0}y^{3}z}{1} \times \dfrac{5y}{2{x}^{5 - 2} {z}^{3} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7Bx%5E%7B0%7Dy%5E%7B3%7Dz%7D%7B1%7D%20%5Ctimes%20%20%5Cdfrac%7B5y%7D%7B2%7Bx%7D%5E%7B5%20-%202%7D%20%7Bz%7D%5E%7B3%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{y^{3}z}{1} \times \dfrac{5y}{2{x}^{3} {z}^{3} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7By%5E%7B3%7Dz%7D%7B1%7D%20%5Ctimes%20%20%5Cdfrac%7B5y%7D%7B2%7Bx%7D%5E%7B3%7D%20%7Bz%7D%5E%7B3%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{y^{3}z {}^{0} }{1} \times \dfrac{5y}{2{x}^{3} {z}^{3 - 1} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7By%5E%7B3%7Dz%20%7B%7D%5E%7B0%7D%20%7D%7B1%7D%20%5Ctimes%20%20%5Cdfrac%7B5y%7D%7B2%7Bx%7D%5E%7B3%7D%20%7Bz%7D%5E%7B3%20-%201%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf\dfrac{y^{3}}{1} \times \dfrac{5y}{2{x}^{3} {z}^{2} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%5Cdfrac%7By%5E%7B3%7D%7D%7B1%7D%20%5Ctimes%20%20%5Cdfrac%7B5y%7D%7B2%7Bx%7D%5E%7B3%7D%20%7Bz%7D%5E%7B2%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf \dfrac{5y \times {y}^{3} }{2{x}^{3} {z}^{2} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%20%20%5Cdfrac%7B5y%20%5Ctimes%20%20%7By%7D%5E%7B3%7D%20%7D%7B2%7Bx%7D%5E%7B3%7D%20%7Bz%7D%5E%7B2%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf \dfrac{5y {}^{0} \times {y}^{3 + 1} }{2{x}^{3} {z}^{2} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%20%20%5Cdfrac%7B5y%20%7B%7D%5E%7B0%7D%20%20%5Ctimes%20%20%7By%7D%5E%7B3%20%2B%201%7D%20%7D%7B2%7Bx%7D%5E%7B3%7D%20%7Bz%7D%5E%7B2%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \sf \dfrac{5 \times {y}^{4} }{2{x}^{3} {z}^{2} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%20%20%5Cdfrac%7B5%20%5Ctimes%20%20%7By%7D%5E%7B4%7D%20%7D%7B2%7Bx%7D%5E%7B3%7D%20%7Bz%7D%5E%7B2%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\dashrightarrow \bf \dfrac{5 {y}^{4} }{2{x}^{3} {z}^{2} }](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Cbf%20%20%5Cdfrac%7B5%20%7By%7D%5E%7B4%7D%20%7D%7B2%7Bx%7D%5E%7B3%7D%20%7Bz%7D%5E%7B2%7D%20%7D)
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
![\therefore \underline{ \textbf{ \textsf{option \red c \: is \: correct}}}](https://tex.z-dn.net/?f=%20%5Ctherefore%20%5Cunderline%7B%20%5Ctextbf%7B%20%5Ctextsf%7Boption%20%5Cred%20c%20%5C%3A%20is%20%5C%3A%20correct%7D%7D%7D)
the thing is I can't see it prop ley:(
Answer:5
Step-by-step explanation:
The equivalent expression for (x + 4)^5 is ![x^5+ 20x^4+ 160x^3 + 640x^2 + 1280x + 1024](https://tex.z-dn.net/?f=x%5E5%2B%2020x%5E4%2B%20160x%5E3%20%2B%20640x%5E2%20%2B%201280x%20%20%2B%201024)
The expression is given as:
![(x + 4)^5](https://tex.z-dn.net/?f=%28x%20%2B%204%29%5E5)
To expand the expression, we make use of Pascal triangle, where:
5:= 1 5 10 10 5 1
So, we have:
![(x + 4)^5 = 1 * x^5 * 4^0 + 5 * x^4 * 4^1 + 10 * x^3 * 4^2 + 10 * x^2 * 4^3 + 5 * x * 4^4 + 1 * x^0 * 4^5](https://tex.z-dn.net/?f=%28x%20%2B%204%29%5E5%20%3D%201%20%2A%20x%5E5%20%2A%204%5E0%20%2B%205%20%2A%20x%5E4%20%2A%204%5E1%20%20%2B%2010%20%2A%20x%5E3%20%2A%204%5E2%20%2B%2010%20%2A%20x%5E2%20%2A%204%5E3%20%2B%205%20%2A%20x%20%2A%204%5E4%20%2B%201%20%2A%20x%5E0%20%2A%204%5E5)
Evaluate the exponents
![(x + 4)^5 = 1 * x^5 * 1 + 5 * x^4 * 4 + 10 * x^3 * 16 + 10 * x^2 * 64 + 5 * x * 256 + 1 *1 * 1024](https://tex.z-dn.net/?f=%28x%20%2B%204%29%5E5%20%3D%201%20%2A%20x%5E5%20%2A%201%20%2B%205%20%2A%20x%5E4%20%2A%204%20%2B%2010%20%2A%20x%5E3%20%2A%2016%20%2B%2010%20%2A%20x%5E2%20%2A%2064%20%2B%205%20%2A%20x%20%2A%20256%20%2B%201%20%2A1%20%2A%201024)
Evaluate the products
![(x + 4)^5 = x^5+ 20x^4+ 160x^3 + 640x^2 + 1280x + 1024](https://tex.z-dn.net/?f=%28x%20%2B%204%29%5E5%20%3D%20x%5E5%2B%2020x%5E4%2B%20160x%5E3%20%2B%20640x%5E2%20%2B%201280x%20%20%2B%201024)
Hence, the equivalent expression for (x + 4)^5 is ![x^5+ 20x^4+ 160x^3 + 640x^2 + 1280x + 1024](https://tex.z-dn.net/?f=x%5E5%2B%2020x%5E4%2B%20160x%5E3%20%2B%20640x%5E2%20%2B%201280x%20%20%2B%201024)
Read more about binomial expressions at:
brainly.com/question/13602562