Grade 8 Exponents: Negative and Fractional Indices
A worksheet covering negative and fractional indices for 8th-grade math students, including simplification and evaluation.
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Grade 8 Exponents: Negative and Fractional Indices
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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?
a⁶
1/a⁶
a⁻¹
1/a²
2. What is the value of (49)^(1/2) * (2)⁻¹?
7
14
3.5
0.5
Simplify the following expression, showing all steps: (x^(1/2) * y⁻³) / (x⁻¹ * y²)