Question

Write the product of the monomials (8x6y)2 and (x3y4).

Answer 1

Answer:

The product of the monomials is 2304 $x^{5}$$y^{6}$

Step-by-step explanation:

* Lets explain how to solve the problem

- We need to find the product of the monomials (8x 6y)² and

   $x^{3}y^{4}$

- At first lets solve the power of the first monomial

- Because the power 2 is on the bracket then each element inside the

  bracket will take power 2

∵ (8x 6y)² = (8)²(x)²(6)²(y)²

∵ (8)² = 64

∵ (x)² = x²

∵ (6)² = 36

∵ (y)² = y²

∴ (8x 6y)² = [64x² × 36y²]

∵ 64 × 36 = 2304 x²y²

∴ The first monomial is 2304 x²y²

∵ The first monomial is 2304 x²y²

∵ The second monomial is $x^{3}y^{4}$

- Lets find their product

- Remember in multiplication if two terms have same bases then we

  will add their powers

∵ [2304 x²y²] × [ $x^{3}y^{4}$ ] =

   2304 [ $x^{2}*x^{3}$ ] [ $y^{2}*y^{4}$ ]

∵ $x^{2}*x^{3}$ = $x^{2+3}$ = $x^{5}$

∵ $y^{2}*y^{4}$ = $y^{2+4}$ = $y^{6}$

∴ [2304 x²y²] × [ $x^{3}y^{4}$ ] = 2304 $x^{5}$$y^{6}$

The product of the monomials is 2304 $x^{5}$$y^{6}$