Negative and Fractional Indices
Explore and practice working with negative and fractional exponents for Grade 7 mathematics.
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Negative and Fractional Indices
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Date:
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. A negative index indicates the of the base number.
2. Any non-zero number raised to the power of zero is equal to .
3. The expression 5⁻² is equivalent to the fraction .
4. Which of the following is equivalent to 3⁻³?
9
1/9
27
1/27
5. Simplify the expression (2⁻¹)⁻².
1/4
4
1/2
2
6. Evaluate 7⁻².
7. Evaluate (1/4)⁻³.
8. A fractional index like x^(1/n) represents the root of x.
9. The expression 8^(1/3) is equivalent to the root of 8.
10. To evaluate 16^(3/2), first find the square root of 16, then the result.
11. Evaluate 25^(1/2).
12. Evaluate 27^(2/3).
Match each expression on the left with its equivalent value on the right.
13. 4⁻²
a. 8
14. 64^(1/3)
b. 1/16
15. 100^(1/2)
c. 10
16. 2³
d. 4
17. The expression (-3)² is equal to -9.
True
False
18. 4^(1/2) is the same as the square root of 4.
True
False
19. Simplify (x⁻³) * (x⁵).
20. What is the value of (1/9)^(-1/2)?