Simplify 4 ^ 13 / (3 ^

To simplify this expression, we need to work on the exponent rules.

First, let's rewrite 4 ^ 13 as (2 ^ 2) ^ 13. According to the power rule, we can multiply the exponents together, so (2 ^ 2) ^ 13 becomes 2 ^ (2 * 13) which is equal to 2 ^ 26.

Next, let's rewrite 3 ^ -5 as 1 / (3 ^ 5) using the negative exponent rule. According to the power rule, 1 / (3 ^ 5) is equal to 1 / (1 * 3 ^ 5) which is equal to 1 / 3 ^ 5.

Now we can rewrite the entire expression as (2 ^ 26) / (1 / 3 ^ 5). Division is the same as multiplying by the reciprocal, so (2 ^ 26) / (1 / 3 ^ 5) is equal to (2 ^ 26) * (3 ^ 5).

To simplify further, we can use the multiplication rule. According to the power rule, (2 ^ 26) * (3 ^ 5) is equal to 2 ^ (26 + 5) which is equal to 2 ^ 31.

Therefore, 4 ^ 13 / (3 ^ - 5) simplifies to 2 ^ 31.

it's wrong

Apologies for the mistake. Let's simplify the expression correctly.

We can simplify 4^13 by using the power rule. Since 4 = 2^2, we can rewrite 4^13 as (2^2)^13, which is equal to 2^(2*13) = 2^26.

Next, let's simplify 3^(-5) using the negative exponent rule. Recall that for any nonzero number a, a^(-n) = 1/(a^n). Therefore, 3^(-5) = 1/(3^5).

Now, let's rewrite the entire expression: 4^13 / (3^(-5)) = (2^26) / (1/(3^5)).
To divide by a fraction, we multiply by the reciprocal. Therefore, (2^26) / (1/(3^5)) = (2^26) * (3^5).

Using the multiplication rule, we can add the exponents: (2^26) * (3^5) = 2^(26+5) = 2^31.

Therefore, the simplified expression is 2^31.