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

Answer 1

#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#.

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Answer 2

Isaiah Anthony

To simplify ( (3bc)^4 ), raise each term inside the parentheses to the fourth power: [ (3bc)^4 = 3^4 \cdot b^4 \cdot c^4 ]

Evaluate ( 3^4 ) to get ( 81 ): [ (3bc)^4 = 81 \cdot b^4 \cdot c^4 ]

So, ( (3bc)^4 ) simplifies to ( 81b^4c^4 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.