Fractional and Negative Indices
Explore and practice fractional and negative indices with this comprehensive Grade 10 math worksheet covering simplification, evaluation, and application.
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Fractional and Negative Indices
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Read each question carefully and show all your working. Simplify all expressions and evaluate numerical answers where possible.
1. Simplify the following expressions, leaving your answers with positive indices:
a) x⁻³
b) 5y⁻²
c) (2a)⁻⁴
2. Evaluate the following expressions without using a calculator:
a) 16^(1/2)
b) 8^(1/3)
c) 27^(2/3)
3. Complete the following statements:
a) x^(a/b) can be written as the b-th root of x raised to the power of .
b) Any non-zero number raised to the power of zero is equal to .
c) To change a negative index to a positive index, you take the of the base.
4. Which of the following is equivalent to (a⁻²)³?
a⁻⁵
a⁻⁶
a⁶
a⁵
5. What is the value of 36^(-1/2)?
6
-6
1/6
-1/6
6. A square has an area of 49x⁻⁴ square units. Find the length of one side of the square.
7. The volume of a cube is 125y⁶ cubic units. Find the length of one edge of the cube.