Negative and Fractional Indices Worksheet

Negative and Fractional Indices

Read each question carefully and show all your work. Simplify all answers to their simplest form.

1. Any non-zero number raised to the power of zero is equal to  .

2. A negative index indicates the   of the base.

3. The expression x^(1/n) is equivalent to the   root of x.

1. Which of the following is equivalent to 5⁻²?

2. Simplify (81)^(1/4).

1. Simplify the following expressions, leaving your answers with positive indices:

a) x⁻⁵

b) (2a³)⁻²

c) (x^(1/3))⁶

d) 9^(3/2)

1. (4x)⁰ = 1, for all real numbers x.

2. The expression (-27)^(1/3) simplifies to -3.

1. If 2^x = 1/16, find the value of x.

2. Evaluate (64/27)^(-2/3).