To simplify the expression [tex]\(a^3 \cdot a^{10}\)[/tex], you can use the laws of exponents. Specifically, when multiplying like bases, you add their exponents.
Step-by-Step Solution:
1. Identify the bases and exponents:
- The base in both terms is [tex]\(a\)[/tex].
- The exponents are 3 and 10.
2. Apply the power rule for multiplication of exponents:
- When you multiply two exponents with the same base, you add the exponents:
[tex]\[
a^3 \cdot a^{10} = a^{3+10}
\][/tex]
3. Add the exponents:
- The sum of the exponents 3 and 10 is 13:
[tex]\[
3 + 10 = 13
\][/tex]
4. Rewrite the expression with the new exponent:
- The simplified form of the expression is:
[tex]\[
a^{13}
\][/tex]
So, the correct simplified form of [tex]\(a^3 \cdot a^{10}\)[/tex] is [tex]\(a^{13}\)[/tex].
Answer: [tex]\(a^{13}\)[/tex]
