Thank you for the opportunity to help you with your question!

c = 2

To do this problem, you have to understand exponent rules:

(x^3)^c = x^(3c)

When you have an exponent to an exponent, you multiply the exponents together. If you look at the right side of the equation, you can see that it is the square of everything on the left hand side of the equation, so 'c' must equal '2'.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Yeah, no problem! Let me know if this helps to clarify the problem at all:

(4x^3 y^5)^c = 16x^6 y^10

When you see that you have a variable on the left hand side of the equation, you need to get the other side of the equation to have the same 'bases' to solve for 'c'.

For example:

Write 16 as a base of 4: 4^2

Write x^6 as a base of x^3: (x^3)^2

Write y^10 as a base of y^5: (y^5)^2

As you can see, they are all squared, so c=2.

If it's still unclear, feel free to send me another example problem that we can work through together :)