Dividing Powers Worksheet
Grade 10 Math worksheet on dividing powers, including simplifying expressions and solving problems involving negative and zero exponents.
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Dividing Powers Worksheet
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Read each question carefully and simplify the expressions involving division of powers. Remember the rules for exponents.
Simplify the following expressions. Show your work.
1. \( \frac{x^8}{x^3} \)
2. \( \frac{y^{12}}{y^4} \)
3. \( \frac{a^5 b^7}{a^2 b^3} \)
4. \( \frac{m^{10} n^3}{m^4 n^3} \)
Choose the correct simplification for each expression.
5. Which expression is equivalent to \( \frac{p^7}{p^{-2}} \)?
\( p^5 \)
\( p^9 \)
\( p^{-5} \)
\( p^{-9} \)
6. What is the simplified form of \( \frac{10^0}{10^3} \)?
\( 10^3 \)
\( 10^{-3} \)
\( 1 \)
\( 0 \)
Complete the statements below.
7. When dividing powers with the same base, you the exponents.
8. Any non-zero number raised to the power of zero is equal to .
9. A negative exponent indicates the of the base.
Indicate whether each statement is True or False.
10. \( \frac{2^6}{2^2} = 2^3 \)
True
False
11. \( (x^3)^2 = x^5 \)
True
False
Solve the following problems.
12. A computer processes data at a rate of \( 2^5 \) operations per second. If a task requires \( 2^9 \) operations, how many seconds will it take to complete the task?
13. Simplify the expression \( \frac{(3^2)^4}{3^5} \).