Quotient Rule of Exponents Practice
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Simplify x675 / x453
.(1 point)
To simplify x675 / x453, we can apply the quotient rule of exponents, which states that when dividing exponential expressions with the same base, subtract the exponents.
In this case, both terms have the base x, so we can simplify the expression as:
x675 / x453 = x^(675-453) = x^222
Therefore, the simplified expression is x^222.
What is the missing exponent in the following equation?
e^?/e^65 = e^38
To find the missing exponent in the equation e^?/e^65 = e^38, we can apply the quotient rule of exponents, which states that when dividing exponential expressions with the same base, we subtract the exponents.
In this case, both terms have the base e, so we can simplify the expression as:
e^?/e^65 = e^(?-65) = e^38
We know that the left side of the equation is equal to the right side, so we can set the exponents equal to each other:
?-65 = 38
We solve for the missing exponent by isolating the variable:
? = 38 + 65
? = 103
Therefore, the missing exponent in the equation is 103.
Simplify 13^12÷13^−10
.
To simplify 13^12 ÷ 13^(-10), we can apply the quotient rule of exponents, which states that when dividing exponential expressions with the same base, we subtract the exponents.
In this case, both terms have the base 13, so we can simplify the expression as:
13^12 ÷ 13^(-10) = 13^(12 - (-10)) = 13^(12 + 10)
We can add the exponents because we are dividing, and a negative exponent is the same as its reciprocal positive exponent.
Therefore, 13^12 ÷ 13^(-10) simplifies to 13^22.
Simplify 4^13÷3^−5
To simplify 4^13 ÷ 3^(-5), we can apply the quotient rule of exponents, which states that when dividing exponential expressions with the same base, we subtract the exponents.
In this case, we have different bases (4 and 3). To simplify, we can rewrite the expression in terms of a common base, which is 4.
To do this, we can convert 3^(-5) into (1/3^5):
4^13 ÷ 3^(-5) = 4^13 ÷ (1/3^5)
Next, we can use the power of a quotient rule to simplify further. The power of a quotient rule states that we can distribute the exponent to the numerator and denominator separately.
4^13 ÷ (1/3^5) = 4^13 × 3^5
Now, we can multiply the bases with the same exponent:
4^13 × 3^5 = (4 × 3)^13
Simplifying further, we have:
(4 × 3)^13 = 12^13
Therefore, 4^13 ÷ 3^(-5) simplifies to 12^13.
incorrect
Apologies for the mistake. Let's start over.
To simplify 4^13 ÷ 3^(-5), we can apply the quotient rule of exponents, which states that when dividing exponential expressions with the same base, we subtract the exponents.
In this case, we have the base 4 and the base 3. Since the bases are different, we cannot simplify by subtracting the exponents.
Therefore, the expression 4^13 ÷ 3^(-5) cannot be further simplified.