Simplify x⁶⁷⁵/x⁴⁵³.
To simplify the expression, we can apply the quotient rule of exponents, which states that when dividing two numbers with the same base, we subtract the exponents.
In this case, since both terms have the base x, we can subtract the exponents:
x^(675-453) = x^222
What is the missing exponent in the following equation?
e^?/e⁶⁵ = e³⁸
To find the missing exponent, we can use the quotient rule of exponents, which states that when dividing two numbers with the same base, we subtract the exponents.
In this case, since both terms have the base e, we can subtract the exponents:
e^(? - 65) = e^38
To solve for the missing exponent, we can set the exponents equal to each other:
? - 65 = 38
Adding 65 to both sides of the equation, we have:
? = 38 + 65
Simplifying, we find:
? = 103
Simplify
13¹² ÷ 13-¹⁰
To simplify this expression, we can use the quotient rule of exponents, which states that when dividing two numbers with the same base, we subtract the exponents.
In this case, we have 13 raised to the 12th power divided by 13 raised to the negative 10th power. Using the quotient rule, we subtract the exponents:
13^(12 - (-10))
When we subtract a negative from a positive exponent, it becomes addition:
13^(12 + 10)
Simplifying the exponent, we have:
13^22
Therefore, 13^12 ÷ 13^-10 simplifies to 13^22.
Simplify
4¹³ ÷ 3-⁵
To simplify this expression, we can apply the quotient rule of exponents, which states that when dividing two numbers with the same base, we subtract the exponents.
In this case, we have 4 raised to the 13th power divided by 3 raised to the negative 5th power. Using the quotient rule, we subtract the exponents:
4^(13 - (-5))
When we subtract a negative from a positive exponent, it becomes addition:
4^(13 + 5)
Simplifying the exponent, we have:
4^18
So, 4^13 ÷ 3^-5 simplifies to 4^18.
Simplify 4¹³ ÷ 3^-5
To simplify the expression 4¹³ ÷ 3⁻⁵, we can use the quotient rule of exponents, which states that when dividing two numbers with the same base, we subtract the exponents.
Therefore, we can rewrite the expression as:
4¹³ / 3⁻⁵
Now, let's simplify the exponents:
4¹³ / (1 / 3⁵)
Since a negative exponent indicates the reciprocal of the base raised to the positive exponent, we can rewrite 3⁻⁵ as 1 / 3⁵.
The expression becomes:
4¹³ / (1 / 3⁵)
4¹³ * 3⁵
Calculating the exponents, we get:
(4^13) * (3^5)
So, the expression 4¹³ ÷ 3⁻⁵ simplifies to (4^13) * (3^5).