e?/e65 = e^38
To solve for e using the equation e/e65 = e^38, we can first multiply both sides of the equation by e65:
e/e65 * e65 = e^38 * e65
Simplifying, we get:
e = e^(38+65)
Using the property of exponential functions that states e^(a+b) = e^a * e^b, we can write:
e = e^38 * e^65
Since e is a constant, we can remove it from both sides:
1 = e^38 * e^65
Now, using the property that states e^a * e^b = e^(a+b), we have:
1 = e^(38+65)
Simplifying the exponent on the right side, we get:
1 = e^103
Therefore, e is equal to 1 raised to the power of 103, which is:
e = 1^103 = 1
Simplify 13^12 ÷ 13^−10
To simplify 13^12 ÷ 13^(-10), you can use the rule of exponentiation that states a^m ÷ a^n = a^(m-n).
Applying this rule, we have:
13^12 ÷ 13^(-10) = 13^(12-(-10)) = 13^(12+10) = 13^22
Therefore, 13^12 ÷ 13^(-10) is equal to 13^22.
Simplify 4^13÷3^−5
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To simplify 4^13 ÷ 3^(-5), we can use the rule of exponentiation that states a^m ÷ a^n = a^(m-n).
Applying this rule, we have:
4^13 ÷ 3^(-5) = 4^13 × 3^5
To multiply these two expressions, we can simply add the exponents:
4^13 × 3^5 = 4^(13+5) × 3^5 = 4^18 × 3^5
Therefore, 4^13 ÷ 3^(-5) simplifies to 4^18 × 3^5.