What is the missing number in this simplified exponential expression: 8^? ÷ 8⁴ = 8¹⁵ ?
A. 11
B. 19
C. 60
D. 8
To find the missing number in the expression 8^? ÷ 8⁴ = 8¹⁵, we can simplify the left side of the equation first.
8^? can be written as 8^1 * 8^4.
Using exponent property that states a^m ÷ a^n = a^(m-n), we can simplify the left side to 8^1 * 8^4 ÷ 8^4, which equals 8^1.
Therefore, the missing number in the expression is 1.
So, the correct answer is D) 8.
Apply the zero power rule to create an equivalent expression to
(-40)⁰+1/2 (11-32⁰)
(-40)⁰+1/2 (11-32⁰) = ? +1/2 (?-?)
According to the zero power rule, any number (except zero) raised to the power of zero equals 1. Therefore, (-40)⁰ is equal to 1.
Applying this rule to the expression:
(-40)⁰ + 1/2 (11 - 32⁰) = 1 + 1/2 (11 - 32⁰)
Now we need to simplify the expression inside the parentheses:
11 - 32⁰ = 11 - 1
Simplifying further:
11 - 1 = 10
Substituting this back into the original expression:
1 + 1/2 (11 - 32⁰) = 1 + 1/2 (10)
Continuing the simplification:
1 + 1/2 (10) = 1 + 1/2 * 10
Further simplification gives us:
1 + 1/2 * 10 = 1 + 5
So, the equivalent expression is:
(-40)⁰ + 1/2 (11 - 32⁰) = 6
To find the missing number in the simplified exponential expression, we need to utilize the property of exponentiation, which states that when dividing two values with the same base, the exponents are subtracted.
Here’s how we can calculate the missing number step-by-step:
1. Start with the equation: 8^? ÷ 8⁴ = 8¹⁵
2. Using the property of exponentiation, we subtract the exponent of 8⁴ from the exponent of 8¹⁵: ? - 4 = 15
3. Simplify the equation by adding 4 to both sides: ? = 15 + 4
4. Calculate the sum: ? = 19
Therefore, the missing number in the simplified exponential expression is 19.
The correct answer is B. 19.
To find the missing number in this simplified exponential expression, we need to use the properties of exponents.
In the given expression, we have:
8^? ÷ 8⁴ = 8¹⁵
Let's break it down step by step:
Step 1: Simplify the expression on the left side of the equation.
Since 8^? is divided by 8⁴, we can subtract the exponents:
8^(? - 4) = 8¹⁵
Step 2: Use the property of exponents that states when the base is the same and the exponents are equal, the bases are equal.
This property tells us that if 8^(? - 4) = 8^15, then ? - 4 = 15.
Step 3: Solve the equation for the missing number (?).
? - 4 = 15
By adding 4 to both sides of the equation, we find:
? = 19
Therefore, the missing number in the simplified exponential expression is 19.
So the answer is option B. 19.