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 (□-□)
(-40)⁰+1/2 (11-32⁰) = 1 + 1/2 (11-1)
= 1 + 1/2 (10)
= 1 + 5
= 6
Can you elaborate further on how you got the answer?
Sure! Let's break down the steps:
1. According to the zero power rule, any number (except zero) raised to the power of zero is equal to 1. So, (-40)⁰ is equal to 1.
2. Next, we simplify the expression within the parentheses: 11-32⁰.
- Again, using the zero power rule, 32⁰ is equal to 1.
- So, 11-32⁰ becomes 11-1, which simplifies to 10.
3. Now, we substitute the simplified values back into the original expression:
- (-40)⁰+1/2 (11-32⁰) becomes 1 + 1/2 (10).
4. Applying the multiplication operation first, we get 1 + 1/2 * 10 = 1 + 5.
5. Finally, adding 1 to 5 gives us the final answer: 6.
Therefore, (-40)⁰+1/2 (11-32⁰) is equivalent to 6.
Which of the following expressions can be simplified to give an answer of 1?
A. (-5.22)⁰
B. 15 - (9.1)⁰
C. 11⁰ + 24⁰
D. 2 (8⁰)
The expression (-5.22)⁰ can be simplified to give an answer of 1 because any number (except zero) raised to the power of zero is equal to 1. Therefore, the correct answer is:
A. (-5.22)⁰
Can you explain the answer further?
Of course! Let's break it down:
In the expression (-5.22)⁰, the base number is -5.22 and it is raised to the power of 0.
According to the zero power rule, any number (except zero) raised to the power of zero is equal to 1.
So, in this case, (-5.22)⁰ simplifies to 1.
Therefore, the expression (-5.22)⁰ can be simplified to give an answer of 1.
Use the power rule to exponents to simplify the expression.
(x⁶)⁵
To simplify the expression (x⁶)⁵ using the power rule for exponents, we multiply the exponents.
The power rule states that when you raise a power to another power, you multiply the exponents.
So in this case, we have (x⁶)⁵ which can be written as x^(6*5) since we multiply the exponents.
Multiplying 6 and 5, we get x^30.
Therefore, the simplified expression is x^30.
To apply the zero power rule, we need to identify any terms with an exponent of zero and simplify them.
In the given expression, the term (-40)⁰ has an exponent of zero. Any number raised to the power of zero is always equal to 1. Therefore, we can simplify (-40)⁰ to 1.
So, the expression (-40)⁰+1/2 (11-32⁰) can be simplified to:
1 + 1/2 (11-32⁰)
Now, let's simplify the expression inside the parentheses, which is 11-32⁰.
Applying the zero power rule again, 32⁰ is equal to 1. Therefore, we can further simplify the expression to:
1 + 1/2 (11-1)
Subtracting 1 from 11, we get:
1 + 1/2 (10)
Finally, let's simplify the remaining fraction by multiplying the numerator and denominator by 1/2:
1/1 + (1/2) * (10/1)
This simplifies to:
1 + 5
Therefore, the equivalent expression to (-40)⁰ + 1/2 (11-32⁰) is:
6