Simplification would be the correct command here.
Step 1: When you have an exponent next to a power that is linked to a parenthesis, it is distributed inside that parenthesis just like when you have the expression 2(x+3) = 2x +6
Remember that exponents multiply when you have an exponent that does not have a base (like 1/2) and it is linked right next to an exponent that does have a base (like 3)
3(631/2t3*1/2) = 3(631/2 t3/2)
That's all to it.
Remember that you cannot multiply inside a parenthesis until that exponent is distributed! For example, you cannot multiply 3 and 63 before you raise 63 to the 1/2 power.
Well, there is nothing to "add" here. We can try and reduce the expression 3(63t^3)^(1/2) to something more manageable.
Whenever you have a power of a power, like (x^2)^3, you multiply the exponents. In the example the result would be x^2*3 which would be x^6. In your problem we have a fractional exponent but not to worry. Do the same operation.First lets deal with the multiplication though:
3(63t^3)^1/2 becomes (189t^3)^1/2
now the multiplication of the exponents
189t^(3*1/2) which is 189t^3/2
now we have to rewrite this expression as 189t^1 + 189t^1/2 to see if we can deal with the fractional exponent again. But there is no perfect square root of 189 so the best we can do is 189t + √189t or we could just leave it as √189t^3. but again, this has nothing to do with adding anything so I'm not sure how to answer the question ultimately.
When you have a power raised to a power like in this question you multiply the powers together (xa)b=x(ab) [different from multiplying powers with the same base where they are added xa*xb=x(a+b)]. So in this case 3(63t3)(1/2)
= 3(631t3)(1/2) because 63=631
= 3((631)(1/2) *(x3)(1/2)) since 63 and x3 are multiplied you can apply the power (1/2) to each individually
= 3(63(1/2) * x(3/2)) Use the exponent power rule to multiply the powers 3*(1/2)=3/2