QQuestionMathematics
QuestionMathematics
Simplify x^3 ⋅x 4 using the product of powers property.
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Step 1:I'll solve this problem step by step using the specified LaTeX formatting guidelines:
Step 2:: Identify the Product of Powers Property
Mathematically, this can be expressed as: $$x^{a} \cdot x^{b} = x^{a+b}
The product of powers property states that when multiplying powers with the same base, we add the exponents.
Step 3:: Apply the Property to the Given Expression
In this problem, we have $$x^{3} \cdot x^{4}
Step 4:: Add the Exponents
x^{3} \cdot x^{4} = x^{3+4}
Step 5:: Simplify the Exponent
x^{3} \cdot x^{4} = x^{7}
Final Answer
Key Insights: - The product of powers property allows us to simplify expressions by adding exponents - This works only when the bases are the same - The result maintains the original base with a new exponent that is the sum of the original exponents
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