what is the missing exponent in the following equation?

3^? / 3^65 = e^38

5 answers

To find the missing exponent, we can use the rule of exponents that states when dividing exponential expressions with the same base, we subtract the exponents.

Therefore, we have:
3^(? - 65) = e^38

Since we want to find the missing exponent, we can set the exponents equal to each other and solve for the missing exponent:
? - 65 = 38

Adding 65 to both sides, we get:
? = 38 + 65

Simplifying, we find that the missing exponent is:
? = 103.
simplify 13^12 divided by 13^-10
To simplify 13^12 divided by 13^-10, we can use the rule of exponents that states when dividing exponential expressions with the same base, we subtract the exponents.

Therefore, we have:
13^12 / 13^-10

Using the rule of subtracting exponents, we have:
13^(12 - (-10))

Simplifying the exponent subtraction, we get:
13^(12 + 10)

Adding the exponents, we have:
13^22
simplify 4^13 divided by 3^-5
To simplify 4^13 divided by 3^-5, we can use the rule of exponents that states when dividing exponential expressions with the same base, we subtract the exponents.

Therefore, we have:
4^13 / 3^-5

Using the rule of subtracting exponents, we have:
4^13 * 3^5

To simplify further, we can calculate the values of 4^13 and 3^5:
4^13 = 67,108,864
3^5 = 243

So, the simplified expression can be written as:
67,108,864 / 243.