Fractional and Negative Indices
Explore fractional and negative indices with this Grade 7 math worksheet, covering simplification and evaluation of expressions.
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Fractional and Negative Indices
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Any non-zero number raised to the power of zero is .
2. A negative index indicates the of the base.
3. The expression \( x^{1/2} \) is equivalent to the of x.
4. \( a^{-n} = \frac{1}{a^n} \) is the rule for indices.
5. Which of the following is equivalent to \( 8^{2/3} \)?
\( \sqrt[3]{8^2} \)
\( \sqrt{8^3} \)
\( 8 \times \frac{2}{3} \)
\( \frac{2}{3 \times 8} \)
6. Evaluate \( 5^{-2} \).
\( -25 \)
\( \frac{1}{25} \)
\( \frac{1}{5} \)
\( 25 \)
7. Simplify the expression: \( \frac{x^5}{x^2} \)
8. Evaluate \( 16^{1/4} \).
9. Write \( \frac{1}{y^3} \) using a negative index.
10. \( (a^m)^n = a^{m+n} \)
True
False
11. \( 9^{1/2} = 3 \)
True
False
12. A square has an area of \( 64^{1/2} \) square units. What is the length of one side of the square? Explain your reasoning.