Question

How does 9^(3/2) = 27?

Answer 1

sqrt(9^3)

sqrt(729)

= 27

Answer 2

How can you figure that without a calculator?

Answer 3

9^3/2=square root of 9^3=square root of 729=27

Answer 4

your exponent is
\[\frac{3}{2}\] the numerator is the "power" and the denominator is the "root" so
\[9^{\frac{3}{2}}=\sqrt{9^3}=3^3=27\]

Answer 5

you can get the same answer by taking powers first, but it is usually easier to take the root first because the numbers are smaller. you probably already knew that the square root of 9 is 3, and that 3 cubed is 27. i doubt you knew what the square root of 729 was

Answer 6

Thank you, that makes sense.