(a^6 x a^6)^k = (a^3)^(k+5)
Solve for k.
a. 3/2
b. 5/3
c. 2
d. 3
e. 5
I think when simplified its (a^12)^k = (a^3)^(k+5)
but i don't know how to get k from here. How do you solve for these kind of exponents?
a^12 = (a^3)^4, so
(a^3)^(4k) = (a^3)^(k+5), so
4k = k+5
k = 5/3
Thank you so much :D
To solve for k in this equation, let's start by simplifying both sides of the equation:
On the left side, (a^6 x a^6) equals a^12 because when you multiply two exponents with the same base, you add their exponents. Therefore, we have (a^12)^k.
On the right side, (a^3)^(k+5) is equal to a^(3(k+5)) because we apply the power of a power property, which states that when you raise a power to another power, you multiply the exponents.
So now we have the equation (a^12)^k = a^(3(k+5)).
To further simplify, we can distribute k through a product. So we have k * 12 = 3(k+5).
Now we can solve for k:
k * 12 = 3k + 15
12k = 3k + 15
Subtracting 3k from both sides:
9k = 15
Dividing both sides by 9:
k = 15/9
Which simplifies to:
k = 5/3
Therefore, the answer is b) 5/3.