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].
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].
