Question

What is the missing number in this simplified exponential expression: 8^? ÷ 8⁴ = 8¹⁵ ?
A. 11
B. 19
C. 60
D. 8

Answer 1

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 (?-?)

Answer 2

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.

Answer 3

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