Question

What value of k makes the equation true? (5a^2 b^3)(6a^k b)=30a^6 b^4

Answer 1

Answer:

k = 4

Step-by-step explanation:

$(5a^2 b^3) (6a^k b) = 30a^6 b^4$

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:

$(5a^2 b^3)(6a^k b)$

= $30a^{2 + k} b^7$

Now we can write it as

$30a^{2 + k} b^7 = 30a^6 b^4$

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.

Answer 2

we are given

$(5a^2 b^3)(6a^k b)=30a^6 b^4$

Firstly, we will simplify left side

and then we can solve for k

Left side is

$(5a^2 b^3)(6a^k b)$

we can arrange like terms

$(5a^2 6a^k)(b^3 b)$

$(5\times 6 a^2a^k)(b^3 b)$

$(30 a^2a^k)(b^3 b^1)$

now, we can use property of exponent

$a^m \times a^n=a^{m+n}$

$(30 a^{2+k})(b^{3+1})$

$30a^{2+k}b^{4}$

now, we can equate it with right side

and we get

$30a^{2+k}b^{4}=30a^6 b^4$

We can see that both sides have 30 , a and b

and they are equal

so, exponent of a must also be equal

$2+k=6$

now, we can solve for k

$2+k-2=6-2$

$k=4$................Answer