Answer :
To simplify the expression [tex]\(x^2 \cdot x^9\)[/tex], you can use the properties of exponents. When multiplying terms that have the same base, you add their exponents. Here's how you can do it:
1. Identify the Base and the Exponents:
- Base: [tex]\(x\)[/tex]
- Exponents: 2 and 9
2. Apply the Property of Exponents:
- The property of exponents tells us that when you multiply like bases, you add the exponents. In mathematical terms, this is written as:
[tex]\[
x^a \cdot x^b = x^{a+b}
\][/tex]
3. Add the Exponents:
- In the expression [tex]\(x^2 \cdot x^9\)[/tex]:
[tex]\[
a = 2 \quad \text{and} \quad b = 9
\][/tex]
- Add these exponents:
[tex]\[
2 + 9 = 11
\][/tex]
4. Write the Simplified Expression:
- Replace the sum of the exponents back into the expression:
[tex]\[
x^{11}
\][/tex]
So, the simplified form of [tex]\(x^2 \cdot x^9\)[/tex] is [tex]\(x^{11}\)[/tex].
1. Identify the Base and the Exponents:
- Base: [tex]\(x\)[/tex]
- Exponents: 2 and 9
2. Apply the Property of Exponents:
- The property of exponents tells us that when you multiply like bases, you add the exponents. In mathematical terms, this is written as:
[tex]\[
x^a \cdot x^b = x^{a+b}
\][/tex]
3. Add the Exponents:
- In the expression [tex]\(x^2 \cdot x^9\)[/tex]:
[tex]\[
a = 2 \quad \text{and} \quad b = 9
\][/tex]
- Add these exponents:
[tex]\[
2 + 9 = 11
\][/tex]
4. Write the Simplified Expression:
- Replace the sum of the exponents back into the expression:
[tex]\[
x^{11}
\][/tex]
So, the simplified form of [tex]\(x^2 \cdot x^9\)[/tex] is [tex]\(x^{11}\)[/tex].
