Question

Simplify 4^13÷3^-5?

Answer 1

To simplify this expression, we can use the properties of exponents.

First, we know that when dividing exponential expressions with the same base, we subtract the exponents. So the expression becomes:

4^13 ÷ 3^(-5) = 4^13 * 3^5

Next, we can use the rule that when multiplying exponential expressions with the same base, we add the exponents. So the expression becomes:

4^13 * 3^5 = 4^13 * 3^5 = 4^13 * (3^3 * 3^2)

Now, we can multiply the exponents:

4^13 * (3^3 * 3^2) = 4^13 * 3^5 = 4^13 * 3^(3+2)

Finally, we can simplify further by multiplying the base 4 with an exponent of 13 and the base 3 with an exponent of 5:

4^13 * 3^(3+2) = 4^13 * 3^5 = 67108864 * 243

So, the simplified expression is 67108864 * 243 or 16,285,859,072.