Use the properties of rational exponents to simplify each expression.

Question

1. 8^2/58^1/5
2. (1/5⁴)²
3. (45^1/2/5^1/2)
4. (40^1/3/5^1/3)⁴
5. 3^-1
6. (5/6)^-2

Answer 1

1. Multiplying two exponential expressions with the same base means you can combine them into one expression with the sum of the bases. So here we end up with 8^3/5.

2. Raising an exponential expression to another power means you can multiply the powers together. Here we end up with 1/5⁸.

3. Here we need to split up the numerator first:

45^1/2/5^1/2

(9*5)^1/2/5^1/2

9^1/2*5^1/2/5^1/2

9^1/2

3

4. This is similar to #3:

(40^1/3/5^1/3)⁴

((8*5)^1/3/5^1/3)⁴

(8^1/3*5^1/3/5^1/3)⁴

(8^1/3)⁴

2⁴

16

5. A negative exponent means to take the inverse of the number, so this just becomes 1/3.

6. Similar to #5:

(5/6)^-2

(6/5)²

36/25