Respuesta :
Answer:
B) a = 3, b = 3 .
Step-by-step explanation:
Given : [tex](2xy)^{4}[/tex] = [tex]4x^{a} (y^{b})4xy[/tex].
To find : Which values of a and b make the equation true.
Solution : We have given that [tex](2xy)^{4}[/tex] = [tex]4x^{a} (y^{b})4xy[/tex].
By exponential same base rule :[tex]x^{n} x^{m} = x^{m+n}[/tex] if base are same then power will be add.
[tex]2^{4} x^{4} y^{4}[/tex] = [tex]16x^{a+1} y^{b+1}[/tex].
Solving exponent
16[tex]x^{4} y^{4}[/tex] = [tex]16x^{a+1} y^{b+1}[/tex].
On equating x variable
[tex]x^{4}[/tex] = [tex]x^{a+1} [/tex].
By exponent rule : if [tex]x^{m}[/tex] = [tex]x^{n} [/tex] then m =n.
So, 4 = a+1
On subtracting by 1 both sides
a = 3.
On equating y variable ,
4 = b+1
On subtracting by 1 both sides
b = 3 .
Therefore, B) a = 3, b = 3 .
The values of a and b that make the equation [tex](2xy)^4=4x^ay^b(4xy)[/tex] to be true are a = 3, b = 3
Solving polynomial equations
The given equation is:
[tex](2xy)^4=4x^ay^b(4xy)[/tex]
Expanding the left hand side, we have:
[tex]16x^4y^4=4x^ay^b(4xy)[/tex]
Simplify the right hand side
[tex]16x^4y^4=16x^{a+1}y^{b+1}[/tex]
Compare the left hand side with the right hand side
a + 1 = 4
a = 4 - 1
a = 3
b + 1 = 4
b = 4 - 1
b = 3
Therefore, the values of a and b that make the equation [tex](2xy)^4=4x^ay^b(4xy)[/tex] to be true are a = 3, b = 3
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