Question
4 to the 13 power divided by 3 to the negative 5 power
Answers
GPT-4o mini
To solve the expression \( \frac{4^{13}}{3^{-5}} \), we first need to apply the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \). Therefore, we can rewrite the expression as follows:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \times 3^{5}
\]
Now we have \( 4^{13} \) multiplied by \( 3^{5} \). We can compute the values as follows:
1. Calculate \( 4^{13} \):
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
(since \( 4 = 2^2 \))
2. Calculate \( 3^{5} \):
\[
3^{5} = 243
\]
Putting it together, we have:
\[
4^{13} \times 3^{5} = 2^{26} \times 243
\]
While we could calculate a numerical value, it is also acceptable to leave the answer in this form. So, the final simplified expression is:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \times 3^{5} = 2^{26} \times 243
\]
If you need the numerical value, we can calculate \( 4^{13} \):
\[
4^{13} = 67,108,864
\]
Then, multiplying this by \( 243 \):
\[
67,108,864 \times 243 = 16,293,857,872
\]
Thus, the numerical final result is:
\[
\frac{4^{13}}{3^{-5}} = 16,293,857,872
\]
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \times 3^{5}
\]
Now we have \( 4^{13} \) multiplied by \( 3^{5} \). We can compute the values as follows:
1. Calculate \( 4^{13} \):
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
(since \( 4 = 2^2 \))
2. Calculate \( 3^{5} \):
\[
3^{5} = 243
\]
Putting it together, we have:
\[
4^{13} \times 3^{5} = 2^{26} \times 243
\]
While we could calculate a numerical value, it is also acceptable to leave the answer in this form. So, the final simplified expression is:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \times 3^{5} = 2^{26} \times 243
\]
If you need the numerical value, we can calculate \( 4^{13} \):
\[
4^{13} = 67,108,864
\]
Then, multiplying this by \( 243 \):
\[
67,108,864 \times 243 = 16,293,857,872
\]
Thus, the numerical final result is:
\[
\frac{4^{13}}{3^{-5}} = 16,293,857,872
\]