What is the missing number in this simplified exponential expression: 8^ ? / 8 ^ 7 =8^ 13
The missing number can be found by subtracting the exponents on both sides of the equation.
8^? / 8^7 = 8^13
Using the property of exponents that states a^m / a^n = a^(m-n), we can rewrite the equation as:
8^(? - 7) = 8^13
By comparing the exponents, we can determine that ? - 7 = 13.
Adding 7 to both sides of the equation, we find:
? = 20
Therefore, the missing number in the simplified exponential expression is 20.
To find the missing number in the simplified exponential expression, let's break down the equation step-by-step:
1. We start with the equation: 8^? / 8^7 = 8^13.
2. We know that when dividing two numbers with the same base, we subtract the exponents. So we have: 8^(? - 7) = 8^13.
3. Since the base is the same, for the exponents to be equal, the expressions inside the parentheses must also be equal. So we have: ? - 7 = 13.
4. To solve for the missing number, we need to isolate it on one side of the equation. Adding 7 to both sides gives us: ? = 13 + 7.
5. Combining like terms, we find that the missing number is: ? = 20.
Therefore, the missing number in the simplified exponential expression is 20.