Product of Powers Worksheet
Practice worksheet for Grade 9 students focusing on the product of powers rule in exponents.
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Product of Powers Rule
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Simplify each expression using the product of powers rule. Show all your work.
1. When multiplying exponents with the same base, you the powers.
2. The product of powers rule states that a^m * a^n = a^( ).
3. The base must be the for the product of powers rule to apply.
4. Simplify: 3^2 * 3^4
5. Simplify: x^5 * x^3
6. Simplify: (2y)^3 * (2y)^6
7. Simplify: a^7 * a^-2
8. Which expression is equivalent to 5^3 * 5^7?
5^21
5^10
25^10
25^21
9. Identify the mistake in the following simplification: 2^3 * 2^5 = 4^8
The exponents were multiplied instead of added.
The bases were multiplied instead of kept the same.
The exponents were subtracted.
There is no mistake; the expression is simplified correctly.
10. The expression (ab)^m * (ab)^n can be simplified to (ab)^(m+n).
True
False
11. The product of powers rule applies only to positive exponents.
True
False
12. Explain in your own words why the product of powers rule works. Provide an example to support your explanation.