How do you simplify #(3bc)^4#?

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Answer 1 · 2015-11-11T08:24:59

#81 b^4 c^4#

What does #(3bc)^4# mean?

Basically, #x^4 = x * x * x * x#, so in your case, it's

#(3bc) ^4 = (3bc) * (3bc) * (3bc) * (3bc)#

As you can multiply in any order your wish, you can drop the parenthesis and "group" the #3#, the #b# and the #c# like follows:

#(3bc) ^4 = (3bc) * (3bc) * (3bc) * (3bc)#
#= 3 * 3 * 3 * 3 * b * b * b * b * c * c * c * c = 3^4 * b^4 * c^4#

Now, the only thing left to do is computing #3^4#:

#3^4 = 9^2 = 81#

So, your solution is #81 b^4 c^4#.