What is the missing exponent in the following equation? e?/e65 = e38
The missing exponent in the equation is -27.
Explanation:
Since this equation involves dividing two exponential expressions with the same base (e), we can subtract the exponents.
The equation e?/e65 = e38 can be rewritten as e(? - 65) = e38.
Therefore, the missing exponent is the value that makes the exponent on e equal to 38.
?(? - 65) = 38
We can solve for ? by setting the exponent equal to 38:
? - 65 = 38
? = 38 + 65
? = 103
So, the missing exponent is 103, making the equation e103/e65 = e38.
To simplify the expression 13^12 ÷ 13^(-10), you can use the properties of exponents.
When dividing with the same base, you subtract the exponents. So, you subtract the exponent of the denominator from the exponent of the numerator.
13^12 ÷ 13^(-10) can be rewritten as 13^(12 - (-10)).
Simplifying the exponent:
12 - (-10) = 12 + 10 = 22.
Therefore, 13^12 ÷ 13^(-10) simplifies to 13^22.
Simplify 13^12÷13−10 .
Simplify 4^13 divided by 3-5
To simplify the expression 4^13 ÷ 3^(-5), you can use the properties of exponents and apply the rules of division.
Recall that dividing with the same base is equivalent to subtracting the exponents. Thus, we can rewrite the expression as:
4^13 ÷ 3^(-5) = 4^13 ÷ (1/3^5).
Simplifying the denominator using the power of a fraction rule, we have:
4^13 ÷ (1/3^5) = 4^13 × 3^5.
Now, we can multiply the bases and add the exponents:
4^13 × 3^5 = (2^2)^13 × 3^5 = 2^(2 × 13) × 3^5 = 2^26 × 3^5.
At this stage, we have simplified the expression as much as possible since no further operations can be performed on the bases. Therefore, the simplified form is 2^26 × 3^5.
whats 2^26 times 3^5
To calculate 2^26 multiplied by 3^5, we multiply the exponents while keeping the base the same:
2^26 multiplied by 3^5 can be written as (2^26) * (3^5).
Using the exponentiation rule for multiplication:
2^26 * 3^5 = 2^(26 + 5) * 3^5.
Adding the exponents:
2^26 * 3^5 = 2^31 * 3^5.
Therefore, the simplified value of 2^26 multiplied by 3^5 is 2^31 * 3^5.