Question
Simplify 4 to the 13 power divided by 3 to the negative 5 power
Answers
GPT-4o mini
To simplify the expression \( \frac{4^{13}}{3^{-5}} \), we can first rewrite the expression using the property of exponents that states \( a^{-n} = \frac{1}{a^n} \).
This means we can rewrite \( 3^{-5} \):
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \times 3^5
\]
Now we have:
\[
4^{13} \times 3^5
\]
Since there are no common bases, this is the simplified form of the expression. If you want to express it in terms of numerical values, you can compute \( 4^{13} \) and \( 3^5 \) separately:
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
\[
3^5 = 243
\]
Thus, you can also express \( 4^{13} \) in terms of base 2. However, the most straightforward simplified form remains:
\[
4^{13} \times 3^5
\]
If you want to compute the numerical value:
1. Calculate \( 4^{13} = 67108864 \)
2. Calculate \( 3^5 = 243 \)
Now multiply these numbers:
\[
67108864 \times 243 = 16284113664546899
\]
Thus, the fully simplified expression in numerical form is \( 16284113664546899 \).
This means we can rewrite \( 3^{-5} \):
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \times 3^5
\]
Now we have:
\[
4^{13} \times 3^5
\]
Since there are no common bases, this is the simplified form of the expression. If you want to express it in terms of numerical values, you can compute \( 4^{13} \) and \( 3^5 \) separately:
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
\[
3^5 = 243
\]
Thus, you can also express \( 4^{13} \) in terms of base 2. However, the most straightforward simplified form remains:
\[
4^{13} \times 3^5
\]
If you want to compute the numerical value:
1. Calculate \( 4^{13} = 67108864 \)
2. Calculate \( 3^5 = 243 \)
Now multiply these numbers:
\[
67108864 \times 243 = 16284113664546899
\]
Thus, the fully simplified expression in numerical form is \( 16284113664546899 \).