e to the power of ?/ e to the power of 65 = e to the power of 38
To find the value of the exponent in the equation e^? / e^65 = e^38, we can simplify the equation by using the properties of exponents and the rules of logarithms.
First, we can rewrite the equation as e^(? - 65) = e^38 by subtracting the exponents on the left side of the equation.
Since the bases of both exponents are equal (e), we can set the exponents equal to each other:
? - 65 = 38
Adding 65 to both sides of the equation:
? = 38 + 65
Simplifying the right side:
? = 103
Therefore, the value of the exponent in the equation is 103.
simplify 13^12 divided by 13^-10
To simplify 13^12 / 13^-10, you can use the rules of exponents and apply the property of dividing exponents with the same base.
First, let's rewrite the division as multiplication with the reciprocal of the denominator:
13^12 * 13^10
Now apply the rule of multiplying exponents with the same base by adding the exponents:
13^(12 + 10)
Simplifying the exponent:
13^22
Therefore, 13^12 / 13^-10 simplifies to 13^22.
simplify 4^13 divided by 3^-5
To simplify (4^13) / (3^(-5)), you can use the rules of exponents.
First, let's rewrite the division as multiplication with the reciprocal of the denominator:
(4^13) * (3^5)
Now apply the rule of multiplying exponents with the same base:
4^13 * 3^5
Next, we can simplify each term separately:
4^13 = (2^2)^13 = 2^(2 * 13) = 2^26
3^5 = 3^(5) = 3^5
Now, we have:
2^26 * 3^5
Therefore, the simplified form of (4^13) / (3^(-5)) is 2^26 * 3^5.
To solve this equation, we can equate the exponents:
e^? / e^65 = e^38
Since the bases are the same (e), we can simplify the equation by subtracting the exponents:
? - 65 = 38
Now, let's solve for ? by adding 65 to both sides:
? = 38 + 65 = 103
Therefore, e^103 / e^65 = e^38.
To solve the equation e^(?)/e^65 = e^38, we can apply the properties of exponents involving division.
First, recall the rule that states "When dividing like bases, subtract the exponents." By applying this rule, we can rewrite the left side of the equation as e^(? - 65).
Therefore, we have e^(? - 65) = e^38.
To solve for ?, we can equate the exponents on both sides.
? - 65 = 38
Next, we can isolate ? by adding 65 to both sides of the equation:
? = 38 + 65
Simplifying further, we get:
? = 103
Hence, in the original equation e^(?)/e^65 = e^38, the value of ? that satisfies the equation is 103.