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------------------------------------------------ Simplify the expression using the properties of exponents.

[tex]x^9 \cdot x^{-4}[/tex]

Answer: [tex]\square[/tex]

Answer :

To simplify the expression [tex]\(x^9 \cdot x^{-4}\)[/tex] using the properties of exponents, follow these steps:

1. Identify the property of exponents: One of the basic properties of exponents is that when you multiply two expressions with the same base, you can add their exponents. This property is expressed as:

[tex]\[
x^a \cdot x^b = x^{a+b}
\][/tex]

2. Apply the property to the expression: In our expression [tex]\(x^9 \cdot x^{-4}\)[/tex], the base is [tex]\(x\)[/tex], and the exponents are 9 and -4. Applying the property, we add the exponents:

[tex]\[
x^9 \cdot x^{-4} = x^{9 + (-4)}
\][/tex]

3. Perform the addition of exponents: Add the exponents 9 and -4:

[tex]\[
9 + (-4) = 5
\][/tex]

4. Write the simplified expression: With the exponent addition complete, the expression simplifies to:

[tex]\[
x^5
\][/tex]

So, the simplified expression is [tex]\(x^5\)[/tex].