What is the missing number in this simplified exponential expression: 7? ÷ 7 and 5 = 7 and 12??
To find the missing number, we need to solve the equation step by step. Given the equation 7? ÷ 7 and 5 = 7 and 12, we can start by evaluating the expression on the left side of the equation, which involves exponentiation and division:
7? ÷ 7 and 5
As no exponent is specified, we can assume it is an exponent of 1. Therefore, 7? is equivalent to 7^1, which is simply 7.
Now our expression becomes:
7 ÷ 7 and 5
Next, proceed with the multiplication before division:
7 ÷ (7 x 5)
Performing the multiplication inside the parentheses:
7 ÷ 35
Finally, evaluate the division:
0.2
Therefore, the missing number is 0.2.
To find the missing number in the simplified exponential expression, let's break down the given expression step by step.
Step 1: Start with the expression 7? ÷ 7 and 5 = 7 and 12??
Step 2: Simplify the left side of the expression: 7? ÷ 7
Step 3: Since any number divided by itself is always equal to 1, we know that 7 ÷ 7 = 1.
Step 4: The expression becomes 1 and 5 = 7 and 12??
Step 5: Since the operation order is from left to right, we can rewrite the expression as 1 = 7 and 12??
Step 6: To solve for the missing number, we need to determine what value makes the equation true.
Step 7: Looking at the right side of the equation, we have 7 and 12. Since there is an "and" between the numbers, it typically represents multiplication.
Step 8: So, 7 and 12 means multiplying the two numbers together, which gives us 84.
Step 9: The expression becomes 1 = 84??
Step 10: Since any number raised to the power of 0 is always equal to 1, we determine that the missing number is 0.
Therefore, the missing number in the given expression is 0.
To find the missing number in the simplified exponential expression, we need to analyze the given equation.
Let's break down the equation step by step:
1. 7 ÷ 7 = 1 (We are dividing 7 by itself, which results in 1.)
2. 1 and 5 = 7 and 12 (This expression can be rewritten as 1^5 = 7^12 because any number raised to the power of 1 gives us the same number.)
Therefore, we have:
1^5 = 7^12
Now, we can solve for the missing number by finding the value of the exponential base.
To do this, we can take the fifth root of both sides of the equation:
(1^5)^(1/5) = (7^12)^(1/5)
This simplifies to:
1 = 7^(12/5)
Now, we need to find the value of 7 raised to the power of (12/5).
By calculating this value, we get:
7^(12/5) ≈ 255.553
So, the missing number in the simplified exponential expression is approximately 255.553.