Simplify exponential expressions worksheet with examples and practice problems.

Let’s solve each problem one by one using the rules of exponents. Remember:

- Any number to the power 0 is 1 (like \( a^0 = 1 \), as long as \( a \neq 0 \)).
- A negative exponent means “flip” the term: \( x^{-n} = \frac{1}{x^n} \) and \( \frac{1}{x^{-n}} = x^n \).
- When multiplying or dividing, combine like bases by adding or subtracting exponents.

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21. \( 4ab^0 = ? \), \( b \neq 0 \)

→ \( b^0 = 1 \), so this becomes \( 4a \cdot 1 = 4a \)

✔ Answer: \( 4a \)

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22. \( \frac{1}{x^{-7}} = ? \)

→ Flip the denominator: \( x^7 \)

✔ Answer: \( x^7 \)

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23. \( 5x^{-4} = ? \)

→ Move \( x^{-4} \) to denominator: \( \frac{5}{x^4} \)

✔ Answer: \( \frac{5}{x^4} \)

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24. \( \frac{1}{c^{-1}} = ? \)

→ Flip: \( c^1 = c \)

✔ Answer: \( c \)

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25. \( \frac{3^{-2}}{n} = ? \)

→ \( 3^{-2} = \frac{1}{9} \), so \( \frac{1/9}{n} = \frac{1}{9n} \)

✔ Answer: \( \frac{1}{9n} \)

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26. \( k^{-4}J^0 = ? \)

→ \( J^0 = 1 \), so we have \( k^{-4} \cdot 1 = \frac{1}{k^4} \)

✔ Answer: \( \frac{1}{k^4} \)

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27. \( \frac{3x^{-2}}{y} = ? \)

→ Move \( x^{-2} \) down: \( \frac{3}{x^2 y} \)

✔ Answer: \( \frac{3}{x^2 y} \)

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28. \( \frac{7ab^{-2}}{3w} = ? \)

→ Move \( b^{-2} \) down: \( \frac{7a}{3w b^2} \)

✔ Answer: \( \frac{7a}{3b^2 w} \)

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29. \( c^{-5}d^{-7} = ? \)

→ Both go to denominator: \( \frac{1}{c^5 d^7} \)

✔ Answer: \( \frac{1}{c^5 d^7} \)

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30. \( c^{-5}d^{7} = ? \)

→ Only \( c^{-5} \) moves down: \( \frac{d^7}{c^5} \)

✔ Answer: \( \frac{d^7}{c^5} \)

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31. \( \frac{8}{2s^{-3}} = ? \)

→ First, simplify numbers: \( \frac{8}{2} = 4 \)

→ Then, \( s^{-3} \) in denominator → move up: \( 4s^3 \)

✔ Answer: \( 4s^3 \)

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32. \( \frac{7s}{5t^{-3}} = ? \)

→ \( t^{-3} \) in denominator → move up: \( \frac{7s t^3}{5} \)

✔ Answer: \( \frac{7s t^3}{5} \)

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33. \( \frac{6a^{-1}c^{-3}}{d^0} = ? \), \( d \neq 0 \)

→ \( d^0 = 1 \), so ignore it.

→ Move \( a^{-1} \) and \( c^{-3} \) down: \( \frac{6}{a c^3} \)

✔ Answer: \( \frac{6}{a c^3} \)

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34. \( 2^{-3}x^2 z^7 = ? \)

→ \( 2^{-3} = \frac{1}{8} \), so \( \frac{x^2 z^7}{8} \)

✔ Answer: \( \frac{x^2 z^7}{8} \)

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35. \( 12^0 t^7 u^7 = ? \)

→ \( 12^0 = 1 \), so just \( t^7 u^7 \)

✔ Answer: \( t^7 u^7 \)

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36. \( \frac{7s^0 t^{-5}}{2^{-1} m^2} = ? \)

→ \( s^0 = 1 \), so numerator: \( 7 \cdot 1 \cdot t^{-5} = \frac{7}{t^5} \)

→ Denominator: \( 2^{-1} = \frac{1}{2} \), so overall denominator is \( \frac{1}{2} m^2 \)

→ So whole expression: \( \frac{7/t^5}{(1/2) m^2} = \frac{7}{t^5} \cdot \frac{2}{m^2} = \frac{14}{t^5 m^2} \)

✔ Answer: \( \frac{14}{t^5 m^2} \)

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Final Answer:
21. \( 4a \)
22. \( x^7 \)
23. \( \frac{5}{x^4} \)
24. \( c \)
25. \( \frac{1}{9n} \)
26. \( \frac{1}{k^4} \)
27. \( \frac{3}{x^2 y} \)
28. \( \frac{7a}{3b^2 w} \)
29. \( \frac{1}{c^5 d^7} \)
30. \( \frac{d^7}{c^5} \)
31. \( 4s^3 \)
32. \( \frac{7s t^3}{5} \)
33. \( \frac{6}{a c^3} \)
34. \( \frac{x^2 z^7}{8} \)
35. \( t^7 u^7 \)
36. \( \frac{14}{t^5 m^2} \)