4 to the power of 13 divided by 3 to the power of -5
To simplify the expression, we can use the laws of exponents:
4^13 / 3^(-5)
When dividing exponents with the same base, subtract the exponent of the denominator from the exponent of the numerator:
4^13 * 3^5
Now, raise 4 to the power of 13 and 3 to the power of 5:
(4^13) * (3^5) = 67108864 * 243
Finally, multiply the two numbers together:
67108864 * 243 = 1632580352
Therefore, 4 to the power of 13 divided by 3 to the power of -5 is equal to 1632580352.
To solve this expression step-by-step, follow these steps:
Step 1: Rewrite the given expression using exponents:
4^13 / 3^-5
Step 2: Apply the rules of exponents:
Recall that when dividing with the same base, you subtract the exponents:
4^(13 - (-5))
Step 3: Simplify the exponents:
4^18
Therefore, the value of 4 to the power of 13 divided by 3 to the power of -5 is equal to 4^18.