Fractional and Negative Indices
A Grade 12 math worksheet focusing on understanding and applying fractional and negative indices in algebraic expressions.
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Fractional and Negative Indices
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Read each question carefully and simplify the expressions involving fractional and negative indices. Show all your work.
1. Simplify the following expressions, leaving your answers with positive indices: a) \(x^4 \cdot x^{-2} \cdot x^{1/2}\) b) \((y^{1/3})^6 \cdot y^{-1}\)
2. Evaluate the following without using a calculator: a) \(16^{3/4}\) b) \(27^{-2/3}\)
3. Which of the following is equivalent to \(\frac{1}{\sqrt[3]{a^2}}\) ?
\(a^{2/3}\)
\(a^{-2/3}\)
\(a^{3/2}\)
\(a^{-3/2}\)
4. The expression \( (8x^6)^{2/3} \) simplifies to .
5. When simplifying \( \frac{12a^5b^{-2}}{3a^2b^{-4}} \), the result is .
Match each expression on the left with its equivalent simplified form on the right.
6. \( (x^2)^{1/2} \)
a. \( \frac{1}{x^{1/2}} \)
7. \( x^{-1/2} \)
b. \( x \)
8. \( \sqrt[3]{x^9} \)
c. \( x^3 \)
9. A rectangular prism has a volume given by \( V = (2x^{1/2})(4x^{-1})(x^{3/2}) \). Simplify the expression for the volume.
10. If \( 3^{2x-1} = 27 \), find the value of \( x \).