Fractional and Negative Indices

Fractional and Negative Indices

Read each question carefully and answer to the best of your ability. Show all your working out where necessary.

1. Which of the following is equivalent to 8^(2/3)?

2. Simplify: (x^-3) * (x^5)

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

2. Any non-zero number raised to a negative exponent is equal to the   of the number raised to the positive exponent.

1. Express (y^(1/2))^4 in its simplest form.

2. Evaluate 27^(-1/3).

1. The expression (4x)^(-2) is equal to 1/(16x^2).

2. When multiplying terms with the same base, you add their exponents, even if they are fractional or negative.

1. Simplify the following expression, leaving your answer with positive indices only: (25x^4y^-2)^(1/2)

2. Write 1/(sqrt(a^3)) in index form.