what is the missing exponent in the following equation? e^?/e^65 = e38
To solve this equation, we can use the properties of exponents. We know that when dividing exponential terms with the same base, we subtract the exponents.
So, when we divide e^? by e^65, we subtract the exponents:
e^?/e^65 = e^(? - 65)
Since the right side of the equation is e^38, we can now set up an equation:
e^(? - 65) = e^38
By equating the exponents, we have:
? - 65 = 38
To isolate the missing exponent, we add 65 to both sides:
? = 38 + 65
Simplifying the expression:
? = 103
Therefore, the missing exponent in the equation is 103.
Simplify 13^12 / 13^-10
To simplify the expression 13^12 / 13^-10, we can use the rule that states when dividing exponential terms with the same base, we subtract the exponents.
So, in this case, we have:
13^12 / 13^-10
To simplify further, we can rewrite 13^-10 as its reciprocal 1/13^10:
13^12 / (1/13^10)
Now, to divide by a fraction, we can multiply by its reciprocal:
13^12 * 13^10
Following the rule for multiplying exponential terms with the same base, we add the exponents:
13^(12+10)
Simplifying the expression:
13^22
Therefore, the simplified form of 13^12 / 13^-10 is 13^22.
simplify 4^13 / 3^-5
To simplify the expression 4^13 / 3^-5, we can follow the same steps as before:
4^13 / 3^-5
Rewrite 3^-5 as its reciprocal 1/3^5:
4^13 / (1/3^5)
Multiply by the reciprocal of the fraction:
4^13 * 3^5
Follow the rule for multiplying exponential terms with the same base, we add the exponents:
4^13 * 3^5 = 4^13 * 3^5
To simplify further, we can leave the answer in this form or calculate the actual value using a calculator.
If you'd like to calculate the value, it would be:
4^13 * 3^5 = 67,108,864 * 243 = 16,318,685,952
So, the simplified form of 4^13 / 3^-5 is 16,318,685,952.
simplify 4^13 divided by 3^-5
To simplify the expression 4^13 divided by 3^-5, we can follow the same steps as before:
4^13 / 3^-5
When dividing exponential terms with the same base, we subtract the exponents:
4^13 / 3^-5 = 4^13 * 3^5
Next, we can simplify the expression by calculating the value using a calculator:
4^13 * 3^5 ≈ 130,606,940,160
So, the simplified form of 4^13 divided by 3^-5 is approximately 130,606,940,160.