Question

Write the following using rational exponents
3√10²
√3 to the -3

Answer 1

3√10² can be written using rational exponents as:

(10²)^(1/3) = 10^(2/3)

Therefore, 3√10² is equal to 10 raised to the power of 2/3.

√3 to the -3 can be written using rational exponents as:

(√3)^(-3/1) = 1 / (√3)^3 = 1 / (3^(1/2))^3 = 1 / 3^(3/2)

Therefore, √3 to the -3 is equal to 1 divided by 3 raised to the power of 3/2.