9 raised to the 1/2 power and 16 raised to the 3/4 power

Asked By Lexi On 02/28/2017 01:24

Answers

Recall that a number raised to a fractional power, i.e. a^(b/c), is the same as taking the c-th root of a and raising it to the power b, or vice-versa. (taking the b-th power of a and then taking the c-th root of that). 9 raised to the 1/2 power, or 9^(1/2), therefore, is the same as taking the second root of 9 and raising it to the first power. The second root, i.e. the square root, of 9 is 3, and 3 raised to the first power is 3. Therefore, 9^(1/2) = 3. 16 raised to the 3/4 power, or 16^(3/4) is the same as taking the fourth root of 16 and raising it to the third power. The fourth root of 16 is 2, and 2 raised to the third power is 8. Therefore, 16^(3/4) = 8.
Answered On 02/28/2017 02:29