we are given
[tex](5a^2 b^3)(6a^k b)=30a^6 b^4[/tex]
Firstly, we will simplify left side
and then we can solve for k
Left side is
[tex](5a^2 b^3)(6a^k b)[/tex]
we can arrange like terms
[tex](5a^2 6a^k)(b^3 b)[/tex]
[tex](5\times 6 a^2a^k)(b^3 b)[/tex]
[tex](30 a^2a^k)(b^3 b^1)[/tex]
now, we can use property of exponent
[tex]a^m \times a^n=a^{m+n}[/tex]
[tex](30 a^{2+k})(b^{3+1})[/tex]
[tex]30a^{2+k}b^{4}[/tex]
now, we can equate it with right side
and we get
[tex]30a^{2+k}b^{4}=30a^6 b^4[/tex]
We can see that both sides have 30 , a and b
and they are equal
so, exponent of a must also be equal
[tex]2+k=6[/tex]
now, we can solve for k
[tex]2+k-2=6-2[/tex]
[tex]k=4[/tex]................Answer
Answer:
k = 4
Step-by-step explanation:
[tex](5a^2 b^3) (6a^k b) = 30a^6 b^4[/tex]
We will solve the right side of the equation to find the value of k which makes this equation true.
Multiplying the terms on the left side of the equation to get:
[tex](5a^2 b^3)(6a^k b)[/tex]
= [tex]30a^{2 + k} b^7[/tex]
Now we can write it as
[tex]30a^{2 + k} b^7 = 30a^6 b^4[/tex]
Now the power of a on the left side (2 + k) should equal the power of a on the right side (6) of the equation to make it true.
2 + k = 6
k = 6 - 2 = 4
Therefore, k = 4 makes the equation true.
