Answer :
Sure! Let's break down the problem step by step.
We have the expression [tex]\(x^4 \cdot x^6\)[/tex], which involves multiplying two powers of the same base, [tex]\(x\)[/tex].
### Step-by-Step Solution:
1. Identify the Base and Exponents:
- In the expression [tex]\(x^4 \cdot x^6\)[/tex], the base is [tex]\(x\)[/tex] for both terms.
- The exponents are 4 and 6.
2. Apply the Laws of Exponents:
- When you multiply powers with the same base, you simply add the exponents. This is one of the laws of exponents, which states:
[tex]\[
x^a \cdot x^b = x^{(a+b)}
\][/tex]
3. Add the Exponents:
- Here, the exponents are 4 and 6. So, you add them together:
[tex]\[
4 + 6 = 10
\][/tex]
4. Write the Result:
- Using the result from adding the exponents, we get:
[tex]\[
x^{10}
\][/tex]
So, the simplified form of [tex]\(x^4 \cdot x^6\)[/tex] is [tex]\(x^{10}\)[/tex].
We have the expression [tex]\(x^4 \cdot x^6\)[/tex], which involves multiplying two powers of the same base, [tex]\(x\)[/tex].
### Step-by-Step Solution:
1. Identify the Base and Exponents:
- In the expression [tex]\(x^4 \cdot x^6\)[/tex], the base is [tex]\(x\)[/tex] for both terms.
- The exponents are 4 and 6.
2. Apply the Laws of Exponents:
- When you multiply powers with the same base, you simply add the exponents. This is one of the laws of exponents, which states:
[tex]\[
x^a \cdot x^b = x^{(a+b)}
\][/tex]
3. Add the Exponents:
- Here, the exponents are 4 and 6. So, you add them together:
[tex]\[
4 + 6 = 10
\][/tex]
4. Write the Result:
- Using the result from adding the exponents, we get:
[tex]\[
x^{10}
\][/tex]
So, the simplified form of [tex]\(x^4 \cdot x^6\)[/tex] is [tex]\(x^{10}\)[/tex].
