What is the missing number in this simplified exponential expression: 8^?÷8^4=8^15 ?(1 point) Responses 11 11 19 19 60 60 8 8
The missing number in the simplified exponential expression is 11.
explain why
To determine the missing number in the simplified exponential expression, we can focus on the exponent property of division, which states that when dividing two exponential expressions with the same base, we can subtract the exponents.
In this case, we have the expression 8^? ÷ 8^4 = 8^15. Since the base is the same (8), we can subtract the exponents.
So, we have ? - 4 = 15. Solving this equation, we add 4 to both sides to isolate the variable on one side:
? = 15 + 4 = 19.
Therefore, the missing number in the simplified exponential expression is 19.
To find the missing value in this exponential expression, we can use the property of exponents that states, "When dividing exponential expressions with the same base, you subtract the exponents."
So in this case, we have:
8^? ÷ 8^4 = 8^15
According to the property, when dividing two exponential expressions with the same base (8 here), we subtract the exponents:
8^(? - 4) = 8^15
To have equal bases, the exponents must be equal:
? - 4 = 15
To solve for the missing number, we can add 4 to both sides of the equation:
? = 15 + 4
This simplifies to:
? = 19
Therefore, the missing number in the simplified exponential expression is 19.