SOLUTION: what is the 6th root of t^2

Question 95209This question is from textbook Precalculus
: what is the 6th root of t^2 This question is from textbook Precalculus

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Taking the 6th root of something is the same as raising it to the power or exponent
.
So taking the 6th root of is the same as raising it to the exponent .
.
This can be written as follows:
.

.
Now you can apply the power rule of exponents. This rule says that when you have a term with
an exponent and you raise that term to an exponent, you multiply the two exponents.
.
In this case, when you have:
.

.
you multiply the exponent times the exponent and the product becomes the
new exponent for t.
.
So we have as the new exponent for t the product: and the answer
becomes:
.

.
Hmm. It appears as if the 1 in the numerator of the exponent is clipped off a little.
Hopefully this doesn't confuse you. But this exponent of 1/3 just tells you to find the
third root (or cube root) of t. And this can be written as:
.

.
Hope this helps you to understand the problem along with providing you some information
about the meaning of fractional exponents and how to apply the power rule for exponents.
RELATED QUESTIONS
what is the 6th root of... (answered by tommyt3rd)

what is the 6th root of 25 to the 5th... (answered by richwmiller)

What is the square root of 9y to the 6th... (answered by mananth,dabanfield)

what is the 6th root of x to the 12... (answered by checkley77)

Solve 2/6th root of 81 (answered by Alan3354)

cube root of 16x to the... (answered by Alan3354,stanbon)

what is another way to write this without the square root part: 6th root of... (answered by stanbon,rothauserc,mananth)

How do you solve 3 times the square root of 20 times T to the 6th... (answered by Fombitz)

For positive real numbers x, y, and z,which of the following expressions is equivalent to (answered by stanbon)