Let's solve the expression step-by-step: [tex]\(\left(3^{0}+4^{-1}\right) \times 2^2\)[/tex]
1. Evaluate [tex]\(3^0\)[/tex]:
- Recall the property that any number to the power of 0 is 1.
- Therefore, [tex]\(3^0 = 1\)[/tex].
2. Evaluate [tex]\(4^{-1}\)[/tex]:
- Recall that [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex].
- Thus, [tex]\(4^{-1} = \frac{1}{4}\)[/tex].
- Therefore, [tex]\(4^{-1} = 0.25\)[/tex].
3. Sum the results of [tex]\(3^0\)[/tex] and [tex]\(4^{-1}\)[/tex]:
- Add the two values calculated in steps 1 and 2.
- [tex]\(1 + 0.25 = 1.25\)[/tex].
4. Evaluate [tex]\(2^2\)[/tex]:
- [tex]\(2^2\)[/tex] means 2 to the power of 2, which is calculated as [tex]\(2 \times 2\)[/tex].
- Therefore, [tex]\(2^2 = 4\)[/tex].
5. Multiply the sum by [tex]\(2^2\)[/tex]:
- Take the result from step 3 and multiply it by the result from step 4.
- [tex]\(1.25 \times 4 = 5.0\)[/tex].
So, the value of the expression [tex]\(\left(3^{0}+4^{-1}\right) \times 2^2\)[/tex] is [tex]\(5.0\)[/tex].
