Let's evaluate the given mathematical expression step-by-step.
We are given the expression:
[tex]\[ 3^3 - 2^{-2} - 7^0 \][/tex]
### Step 1: Evaluate each power
1. Evaluate [tex]\( 3^3 \)[/tex]:
[tex]\[ 3^3 = 3 \times 3 \times 3 = 27 \][/tex]
2. Evaluate [tex]\( 2^{-2} \)[/tex]:
By definition of negative exponents, [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex].
[tex]\[ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} = 0.25 \][/tex]
3. Evaluate [tex]\( 7^0 \)[/tex]:
By the properties of exponents, any number raised to the power of 0 is 1.
[tex]\[ 7^0 = 1 \][/tex]
### Step 2: Substitute the evaluated terms into the original expression
Now we substitute these values back into the expression:
[tex]\[ 27 - 0.25 - 1 \][/tex]
### Step 3: Perform the arithmetic operations
1. First, subtract 0.25 from 27:
[tex]\[ 27 - 0.25 = 26.75 \][/tex]
2. Then, subtract 1 from 26.75:
[tex]\[ 26.75 - 1 = 25.75 \][/tex]
### Conclusion
The value of the expression [tex]\( 3^3 - 2^{-2} - 7^0 \)[/tex] is:
[tex]\[ 25.75 \][/tex]
