Question
Use the product rule of exponents to simplify 13to the power of 10 and 13 to the power of 4
Answers
GPT-4o mini
To simplify the expression \( 13^{10} \times 13^4 \) using the product rule of exponents, you add the exponents when multiplying like bases. The product rule states that:
\[
a^m \times a^n = a^{m+n}
\]
For your specific case:
\[
13^{10} \times 13^4 = 13^{10 + 4}
\]
Now adding the exponents:
\[
10 + 4 = 14
\]
So, we have:
\[
13^{10} \times 13^4 = 13^{14}
\]
Thus, the simplified form is:
\[
13^{14}
\]
\[
a^m \times a^n = a^{m+n}
\]
For your specific case:
\[
13^{10} \times 13^4 = 13^{10 + 4}
\]
Now adding the exponents:
\[
10 + 4 = 14
\]
So, we have:
\[
13^{10} \times 13^4 = 13^{14}
\]
Thus, the simplified form is:
\[
13^{14}
\]