Algebra multiplying sq rt

I need to use rational exponents to write the answer to:
the cube root of x times the 4 root of 7x.
there is a rule when the numbers on the radicand are different, yes?

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1. I multiply the sq rt numbers to get 12 yes? and then do I multiply the x times 7x to get 7x^7?

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2. x^(1/3) * (7x)^(1/4)

= x^(1/3) * 7^(1/4) * x^(1/4)

= 7^(1/4) * x(1/3 + 1/4)

= 7^(1/4) * x (7/12)
In other words, when you multiply you add exponents
think
10^1 * 10^2 = 10^3 = 1,000
like you know that
10 * 100 = 1000

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