Use the Product Rule of Exponents to simplify the expression 2^4 ⋅2^2.
To simplify the expression 2^4 ⋅ 2^2 using the Product Rule of Exponents, we add the exponents when multiplying two numbers with the same base.
2^4 ⋅ 2^2 = 2^(4+2) = 2^6
Therefore, the simplified expression is 2^6.
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(5^2) 9
10^8⋅10^8
32^7
6^2⋅7^3
The expression that is correctly developed to use the Product Rule of Exponents is:
10^8 ⋅ 10^8
Simplify x^675/x^453
To simplify x^675 / x^453, we can use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, x^675 / x^453 = 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 use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, e^?/e^65 = e^(?-65) = e^38.
To solve for the missing exponent, we can set the exponents equal to each other:
?-65 = 38.
To isolate the missing exponent, we can add 65 to both sides:
?-65 + 65 = 38 + 65.
This simplifies to:
? = 103.
Therefore, the missing exponent in the equation is 103.
Simplify 13^12÷13^−10
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To simplify 13^12 ÷ 13^(-10), we can use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, 13^12 ÷ 13^(-10) = 13^(12 - (-10)) = 13^(12 + 10) = 13^22.
Therefore, the simplified expression is 13^22.