Simplify 4 ^ 13 / 3 ^ -5
To simplify the expression 4^13 / 3^-5, we can apply the properties of exponents.
First, we can use the rule that states a^m / a^n = a^(m-n).
So, 4^13 / 3^-5 can be rewritten as 4^13 * 3^5.
Next, we can multiply the bases together and add the exponents, so we have 4^13 * 3^5 = 4^13 * 3^5.
Finally, we can multiply the powers of the bases, so 4^13 * 3^5 = (4*4*4*4*4*4*4*4*4*4*4*4*4) * (3*3*3*3*3).
This can be simplified to: 67,108,864 * 243.
To simplify the expression 4^13 / 3^(-5), we can use the properties of exponents.
First, let's simplify each exponent separately:
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4
= 67,108,864
3^(-5) = 1 / 3^5
= 1 / (3 * 3 * 3 * 3 * 3)
= 1 / 243
= 0.00411522634 (rounded to 11 decimal places)
Now that we have simplified the exponents, we can divide:
4^13 / 3^(-5) = 67,108,864 / 0.00411522634
≈ 16,296,140,524.27 (rounded to 2 decimal places)
Therefore, the simplified form of the expression 4^13 / 3^(-5) is approximately 16,296,140,524.27.