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(63^{1/2}t^{3*1/2}) = 3(63^{1/2} t^{3/2})

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.

Chris S. | ESL, English, math, biblical studies, computer, philosophyESL, English, math, biblical studies, co...

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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 (x^{a})^{b}=x^{(ab) }[different from multiplying powers with the same base where they are added x^{a}*x^{b}=x^{(a+b)}]. So in this case 3(63t^{3})^{(1/2)}

= 3(63^{1}t^{3})^{(1/2) } because 63=63^{1}

= 3((63^{1})^{(1/2)}^{ }*(x^{3})^{(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