Grade 8 Exponents: Negative and Fractional Indices

Grade 8 Exponents: Negative and Fractional Indices

Read each question carefully and simplify or evaluate the expressions involving negative and fractional indices. Show all your work.

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

2. To simplify an expression with a negative exponent, move the base to the   of the fraction and change the sign of the exponent.

3. The expression x⁻³ can be written as  .

1. Simplify: 5⁻²

2. Simplify: (2/3)⁻³

3. Simplify: x⁴y⁻²

1. An expression with a fractional exponent, such as x^(1/n), can be written as the   root of x.

2. The expression 8^(1/3) is equivalent to the   root of 8.

3. When an exponent is a fraction m/n, it means taking the   root and then raising the result to the power of  .

1. Evaluate: 16^(1/2)

2. Evaluate: 27^(1/3)

3. Evaluate: 64^(2/3)

1. Which of the following is equivalent to (a⁻²)³?

2. What is the value of (49)^(1/2) * (2)⁻¹?

Simplify the following expression, showing all steps: (x^(1/2) * y⁻³) / (x⁻¹ * y²)