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.
what is the missing exponent in the following equation? e^?/e^65 = e38
7 answers
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.
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.
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.
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.
3 answers