Answer:
The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
Step-by-step explanation:
* Lets explain how to solve the problem
- We need to find the product of the monomials (8x 6y)² and
[tex]x^{3}y^{4}[/tex]
- 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 [tex]x^{3}y^{4}[/tex]
- Lets find their product
- Remember in multiplication if two terms have same bases then we
will add their powers
∵ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] =
2304 [ [tex]x^{2}*x^{3}[/tex] ] [ [tex]y^{2}*y^{4}[/tex] ]
∵ [tex]x^{2}*x^{3}[/tex] = [tex]x^{2+3}[/tex] = [tex]x^{5}[/tex]
∵ [tex]y^{2}*y^{4}[/tex] = [tex]y^{2+4}[/tex] = [tex]y^{6}[/tex]
∴ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] = 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
