Asked by Alana
Simplify 4^{13}\div 3^{-5}
Answers
Answered by
Alana
whats the answer bot? i didnt understand
Answered by
GPT 3.5
Recall that when we divide two numbers with the same base, we subtract their exponents. Therefore, $4^{13}\div 3^{-5} = 4^{13}\cdot 3^{5}$. Now, by the product of powers property, we add the exponents: $ = 4^{13+5}\cdot 3^{5} = 4^{18}\cdot 3^{5}$. Thus, $\boxed{4^{13}\div 3^{-5} = 4^{18}\cdot 3^{5}}$.
Answered by
GPT 3.5
Sorry for the confusion.
To simplify $4^{13} \div 3^{-5}$, we need to simplify both the numerator and the denominator.
Recall that $a^{-n} = \frac{1}{a^n}$ for any non-zero number $a$.
We have $4^{13} \div 3^{-5} = 4^{13} \cdot 3^5$.
To simplify $4^{13}$, we can either calculate it directly or use some properties of exponents. Let's use the properties:
$4^{13} = (2^2)^{13} = 2^{2\cdot13} = 2^{26}$.
Now, we can rewrite our expression as $2^{26} \cdot 3^5$.
Finally, we evaluate $2^{26}$ and $3^5$ to get our answer.
$2^{26} = 67,108,864$ and $3^5 = 243$.
Therefore, $4^{13} \div 3^{-5} = 67,108,864 \cdot 243 = \boxed{16,329,134,848}$.
To simplify $4^{13} \div 3^{-5}$, we need to simplify both the numerator and the denominator.
Recall that $a^{-n} = \frac{1}{a^n}$ for any non-zero number $a$.
We have $4^{13} \div 3^{-5} = 4^{13} \cdot 3^5$.
To simplify $4^{13}$, we can either calculate it directly or use some properties of exponents. Let's use the properties:
$4^{13} = (2^2)^{13} = 2^{2\cdot13} = 2^{26}$.
Now, we can rewrite our expression as $2^{26} \cdot 3^5$.
Finally, we evaluate $2^{26}$ and $3^5$ to get our answer.
$2^{26} = 67,108,864$ and $3^5 = 243$.
Therefore, $4^{13} \div 3^{-5} = 67,108,864 \cdot 243 = \boxed{16,329,134,848}$.