ASVAB Study GuideProduct Rule
Multiplying terms with the same base.
$$x^a \cdot x^b = x^{a+b}$$
Keep the base and add the exponents.
Example
Simplify:
$$x^4 \cdot x^5$$
Show solution
- Step 1: Identify same base 'x'.
- Step 2: Add exponents: $$4 + 5 = 9$$.
- Step 3: Write result: $$x^9$$.
=> Conclusion: $$x^4 \cdot x^5 = x^9$$
Practice problems
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Problem 1
Simplify:
$$x^3 \cdot x^6$$
Show solution
Answer: $$x^9$$
- Step 1: Keep base 'x'.
- Step 2: Add exponents: $$3 + 6 = 9$$.
=> Conclusion: $$x^9$$.
=> Correct Option: B ($$x^9$$).
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Problem 2
Simplify:
$$(2x^4)(5x^3)$$
Show solution
Answer: $$10x^7$$
- Step 1: Multiply coefficients: $$2 \cdot 5 = 10$$.
- Step 2: Apply Product Rule for variables: $$x^{4+3} = x^7$$.
- Step 3: Combine: $$10x^7$$.
=> Conclusion: $$10x^7$$.
=> Correct Option: A ($$10x^7$$)
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Problem 3
Simplify:
$$(3x^2y^5)(4x^3y^2)$$
Show solution
Answer: $$12x^5y^7$$
- Step 1: Multiply coefficients: $$3 \cdot 4 = 12$$.
- Step 2: Add exponents for x: $$x^{2+3} = x^5$$.
- Step 3: Add exponents for y: $$y^{5+2} = y^7$$.
- Step 4: Combine: $$12x^5y^7$$.
=> Conclusion: $$12x^5y^7$$.
=> Correct Option: B ($$12x^5y^7$$)