Convert the following to a rational exponent. What is your exponent in simplest form?
cuberoot(9^12)
a).3/12
b).1/4
c).4
d).12/3
I think the answer is is d.
Would i have to simplify the fraction for the exponent? I know you are supposed to simplify, but I did not know if that was the case for this one. Because if 4 was the exponent, you would not be able to put the answer as cuberoot(9^12)
cuberoot(9^12)
= (9^12)^(1/3)
= 9^4
so what is the new exponent?
To convert the given expression to a rational exponent, you need to rewrite the cube root as an exponent with a fractional power. The fractional exponent will have the cube root as its numerator and the exponent as its denominator.
So, we can rewrite the expression as:
(9^12)^(1/3)
According to the exponentiation rule, when you raise a power to another power, you need to multiply the exponents. So, in this case, we multiply the exponents to get:
9^(12 * 1/3)
Since 12 * 1/3 is equal to 4, the expression simplifies to:
9^4
Therefore, the exponent in simplest form is 4.
So, the correct answer is option c) 4.