Simplify x^675/x^453
To simplify x^675/x^453, we can subtract the exponents since we are dividing the terms with the same base:
x^(675-453)
Simplifying further:
x^222
Find ?
e^?/e^65=e^38
To solve for the missing value, we can use the property of exponents that states:
(e^(a))/e^(b) = e^(a-b)
Using this property, we can rewrite the equation as:
e^(? - 65) = e^38
Now, we can set the exponents equal to each other:
? - 65 = 38
Solving for ?, we add 65 to both sides of the equation:
? = 38 + 65
? = 103
Simplify 13^12÷13^-10
To simplify 13^12 ÷ 13^-10, we can use the rule of exponentiation that states:
a^m ÷ a^n = a^(m - n)
Applying this rule to our expression, we can rewrite it as:
13^(12 - (-10))
Simplifying the exponents:
13^(12 + 10)
13^22
Simplify 4^13÷3^-5
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 to our expression, we can rewrite it as:
4^13 ÷ 3^-5 = 4^13 × 3^5
Simplifying the exponents:
= 4^13 × (3^5)
Remembering that when multiplying numbers with the same base, we add the exponents, we have:
= 4^13 × (3^5) = 4^13 × 3^5 = 4^13 × 243
The expression is now simplified to 4^13 × 243.
4^13×243
The simplified expression 4^13 × 243 can be further simplified by evaluating the exponents and multiplying the numbers:
4^13 × 243 = 67,108,864 × 243 = 16,342,315,904.