Certainly! Let's go through the steps to evaluate the expression [tex]\(1.2^3 + (-1.9)^4\)[/tex] and find its value to the nearest tenth.
1. Evaluate [tex]\(1.2^3\)[/tex]:
We need to calculate [tex]\(1.2\)[/tex] raised to the power of [tex]\(3\)[/tex]:
[tex]\[
1.2^3 = 1.2 \times 1.2 \times 1.2 = 1.728
\][/tex]
Therefore, [tex]\(1.2^3 = 1.728\)[/tex].
2. Evaluate [tex]\((-1.9)^4\)[/tex]:
Next, we calculate [tex]\((-1.9)\)[/tex] raised to the power of [tex]\(4\)[/tex]:
[tex]\[
(-1.9)^4 = (-1.9) \times (-1.9) \times (-1.9) \times (-1.9) = 13.0321
\][/tex]
While squaring [tex]\(-1.9\)[/tex] twice, we observe that multiplying a negative number an even number of times yields a positive result.
3. Add the two values together:
Sum the results from the previous steps:
[tex]\[
1.728 + 13.0321 = 14.7601
\][/tex]
Therefore, the value of [tex]\(1.2^3 + (-1.9)^4\)[/tex] is [tex]\(14.7601\)[/tex].
4. Round to the nearest tenth:
To round [tex]\(14.7601\)[/tex] to the nearest tenth, we look at the hundredths place (the second digit after the decimal point):
- If the hundredths place is 5 or greater, we round up.
- If the hundredths place is less than 5, we round down.
In this case, the hundredths place is 6, so we round up:
[tex]\[
14.7601 \approx 14.8
\][/tex]
Thus, the value of [tex]\(1.2^3 + (-1.9)^4\)[/tex] to the nearest tenth is [tex]\(14.8\)[/tex].
