What is the missing exponent in the following equation? e^?/(e^65)=e^38
The missing exponent in the equation is 27.
are you sure?
Apologies, I made a mistake in my previous response.
To solve the equation e^?/(e^65) = e^38, we can use the property of subtracting exponents.
Converting both sides of the equation to have the same base, we have:
e^(? - 65) = e^38
Since the bases are equal, we can equate the exponents:
? - 65 = 38
Solving for ?, we add 65 to both sides:
? = 38 + 65
Therefore, the missing exponent is 103.
Simplify 13^12÷13^−10
To simplify 13^12 ÷ 13^(-10), we can apply the rule of subtracting exponents with the same base.
Using the formula a^m ÷ a^n = a^(m - n), we have:
13^(12 - (-10))
Simplifying the exponent, we have:
13^(12 + 10)
Therefore, 13^12 ÷ 13^(-10) simplifies to 13^22.
Simplify 4^13÷3^−5
To simplify 4^13 ÷ 3^(-5), we can apply the rule of subtracting exponents with the same base.
Using the formula a^m ÷ a^n = a^(m - n), we have:
4^13 ÷ 3^(-5)
Since the bases are different, we cannot subtract the exponents directly. Instead, we can write 3^(-5) as the reciprocal of 3^5:
4^13 ÷ (1 / 3^5)
Simplifying the reciprocal, we have:
4^13 × 3^5
Now, we can multiply the expressions with the same base:
4^13 × 3^5 = 4^13 × 3^5
Therefore, 4^13 ÷ 3^(-5) simplifies to 4^13 × 3^5.
are you sure?
Apologies for the incorrect response.
To simplify 4^13 ÷ 3^(-5), we can apply the rule of subtracting exponents with the same base.
Using the formula a^m ÷ a^n = a^(m - n), we have:
4^13 ÷ 3^(-5)
Since dividing by a negative exponent is the same as multiplying by the positive exponent, we can rewrite the expression as:
4^13 × 3^5
Now, we can simplify the expression by multiplying the numbers with the same base:
4^13 × 3^5
Therefore, 4^13 ÷ 3^(-5) simplifies to 4^13 × 3^5.