Alright, let's solve the given mathematical expressions step-by-step.
### (a) [tex]\((-6)^2 + 13^3 + (-7)^3\)[/tex]
1. Calculate [tex]\((-6)^2\)[/tex]:
[tex]\[
(-6)^2 = 36
\][/tex]
2. Calculate [tex]\(13^3\)[/tex]:
[tex]\[
13^3 = 13 \times 13 \times 13 = 169 \times 13 = 2197
\][/tex]
3. Calculate [tex]\((-7)^3\)[/tex]:
[tex]\[
(-7)^3 = (-7) \times (-7) \times (-7) = 49 \times (-7) = -343
\][/tex]
4. Sum the results:
[tex]\[
36 + 2197 + (-343) = 36 + 2197 - 343 = 36 + 1854 = 1890
\][/tex]
So, the value of [tex]\((-6)^2 + 13^3 + (-7)^3\)[/tex] is [tex]\(\boxed{1890}\)[/tex].
### (b) [tex]\((-21)^3 + 28^3\)[/tex]
1. Calculate [tex]\((-21)^3\)[/tex]:
[tex]\[
(-21)^3 = (-21) \times (-21) \times (-21) = 441 \times (-21) = -9261
\][/tex]
2. Calculate [tex]\(28^3\)[/tex]:
[tex]\[
28^3 = 28 \times 28 \times 28 = 784 \times 28 = 21952
\][/tex]
3. Sum the results:
[tex]\[
-9261 + 21952 = 21952 - 9261 = 12691
\][/tex]
So, the value of [tex]\((-21)^3 + 28^3\)[/tex] is [tex]\(\boxed{12691}\)[/tex].
