Product of Powers Worksheet
Grade 12 Math worksheet focusing on the product of powers rule for exponents, including simplification and problem-solving.
Includes
Standards
Topics
Product of Powers Rule
Name:
Date:
Score:
Read each question carefully and simplify the expressions using the product of powers rule. Show all your work.
Simplify the following expressions:
1. \(x^3 \cdot x^5\)
2. \(a^7 \cdot a^{-2}\)
3. \(y^{1/2} \cdot y^{3/2}\)
4. \((2m^4)(3m^2)\)
5. Which of the following is equivalent to \(b^p \cdot b^q\)?
\(b^{p-q}\)
\(b^{p \cdot q}\)
\(b^{p+q}\)
\((b^p)^q\)
6. Simplify: \(4^k \cdot 4^{2k+1}\)
\(4^{2k^2+k}\)
\(4^{3k+1}\)
\(16^{3k+1}\)
\(4^{2k+1}\)
Complete the following statements:
7. When multiplying powers with the same base, you the exponents.
8. The expression \((p^3)(p^x)\) simplifies to \(p^9\) if \(x =\) .
Indicate whether each statement is True or False:
9. \( (2x^2)(3x^3) = 6x^5 \)
True
False
10. \( (a^4)(b^2) = (ab)^6 \)
True
False
11. The area of a rectangular garden is given by the expression \( (4x^2)(2x^3) \) square meters. What is the simplified expression for the area of the garden?
12. A scientist observes a bacterial colony that doubles its size every hour. If the initial size of the colony is \(2^5\) cells, what will be the size of the colony after 3 hours? Express your answer using exponents.