Apply the Zero Power Rule to create an equivalent expression to (−20)^0 + 1/2(18−6^0) (2 points)
The Zero Power Rule states that any number (except 0) raised to the power of 0 is equal to 1.
Using this rule, we can apply it to the expression:
(-20)^0 + 1/2(18 - 6^0)
Since (-20)^0 is equal to 1, we can simplify the expression:
1 + 1/2(18 - 1)
Simplifying further:
1 + 1/2(17)
Multiplying 1/2 by 17:
1 + 17/2
Adding the fractions:
1 + 8.5
Simplifying the sum:
9.5
Therefore, the equivalent expression is 9.5.
To apply the Zero Power Rule, we need to rewrite any bases raised to the power of zero as 1.
Let's begin by rewriting the expression step by step:
1. Start with the original expression: (-20)^0 + 1/2(18 - 6^0)
2. Apply the Zero Power Rule to (-20)^0: 1 + 1/2(18 - 1)
3. Simplify the expression within the parentheses: 1 + 1/2(17)
4. Multiply 1/2 by 17: 1 + 17/2
5. Find a common denominator for 1 and 17/2: 2/2 + 17/2
6. Add the fractions: (2 + 17)/2 = 19/2
Therefore, the equivalent expression applying the Zero Power Rule is 19/2.
To apply the Zero Power Rule, we must first understand what it involves. The Zero Power Rule states that any number (except for zero) raised to the power of zero is equal to 1. In other words, for any nonzero number 'a', a^0 = 1.
Now, let's break down the given expression step by step:
(−20)^0 + 1/2(18−6^0)
Step 1: Evaluate (-20)^0 using the Zero Power Rule.
(-20)^0 = 1
Step 2: Simplify the second part of the expression.
1/2(18−6^0) = 1/2(18−1) [Since 6^0 = 1]
Step 3: Simplify further.
1/2(18−1) = 1/2(17) = 17/2
Step 4: Combine the simplified expressions.
1 + 17/2 = 1 + 8.5 = 9.5
So, the equivalent expression to (−20)^0 + 1/2(18−6^0) is 9.5.