Answered

I am unable to make sense of the original problem as it is written. Here is an attempt to rewrite it in a coherent manner:

Solve the following expressions:

1. [tex]\(2(x)^3\)[/tex]
2. [tex]\(1(2x)^3\)[/tex]
3. [tex]\((4x^3)^2\)[/tex]
4. [tex]\(15(-3m^2n)^2\)[/tex]
5. [tex]\(2(3x^3)^2\)[/tex]
6. [tex]\(23 - (-6y^2)\)[/tex]
7. [tex]\(24 - (-6y)^2\)[/tex]
8. [tex]\(26 - 2(-3n^2)^2\)[/tex]
9. [tex]\(30 - (-3y)^3\)[/tex]
10. [tex]\(\left[-2(-2a^3)\right]^3\)[/tex]

Note: Please verify that these are the expressions intended for simplification or evaluation, as the original text may contain errors or omissions.



Answer :

GinnyAnswer
Sure! Let's work through each expression step-by-step:

1. Expression: [tex]\(2(x)^3\)[/tex]

- Substitute [tex]\(x = 1\)[/tex].
- Compute [tex]\(2(1)^3 = 2 \cdot 1 = 2\)[/tex].

Result: [tex]\(2\)[/tex]

2. Expression: [tex]\(1(2x)^3\)[/tex]

- Substitute [tex]\(x = 1\)[/tex].
- Compute [tex]\(1(2 \cdot 1)^3 = 1 \cdot 2^3 = 1 \cdot 8 = 8\)[/tex].

Result: [tex]\(8\)[/tex]

3. Expression: [tex]\(1(4x^3)^2\)[/tex]

- Substitute [tex]\(x = 1\)[/tex].
- Compute [tex]\(1(4(1)^3)^2 = 1(4 \cdot 1)^2 = 1 \cdot 4^2 = 1 \cdot 16 = 16\)[/tex].

Result: [tex]\(16\)[/tex]

4. Expression: [tex]\(15(-3m^2 n)^2\)[/tex]

- Substitute [tex]\(m = 1\)[/tex] and [tex]\(n = 1\)[/tex].
- Compute [tex]\(15(-3(1)^2 (1))^2 = 15(-3 \cdot 1 \cdot 1)^2 = 15(-3)^2 = 15 \cdot 9 = 135\)[/tex].

Result: [tex]\(135\)[/tex]

5. Expression: [tex]\(21(2(3x^3)^2)\)[/tex]

- Substitute [tex]\(x = 1\)[/tex].
- Compute [tex]\(21(2(3(1)^3)^2) = 21(2(3 \cdot 1)^2) = 21(2 \cdot 3^2) = 21(2 \cdot 9) = 21 \cdot 18 = 18\)[/tex].

Result: [tex]\(18\)[/tex]

6. Expression: [tex]\(23 - (-6y^2)\)[/tex]

- Substitute [tex]\(y = 1\)[/tex].
- Compute [tex]\(23 - (-6(1)^2) = 23 - (-6 \cdot 1) = 23 - (-6) = 23 + 6 = 29\)[/tex].

Result: [tex]\(29\)[/tex]

7. Expression: [tex]\(24 - (-6y)^2\)[/tex]

- Substitute [tex]\(y = 1\)[/tex].
- Compute [tex]\(24 - (-6 \cdot 1)^2 = 24 - (-6)^2 = 24 - 36 = -12\)[/tex].

Result: [tex]\(-12\)[/tex]

8. Expression: [tex]\(26 - 2(-3n^2)^2\)[/tex]

- Substitute [tex]\(n = 1\)[/tex].
- Compute [tex]\(26 - 2(-3(1)^2)^2 = 26 - 2(-3 \cdot 1)^2 = 26 - 2(-3)^2 = 26 - 2 \cdot 9 = 26 - 18 = 8\)[/tex].

Result: [tex]\(8\)[/tex]

9. Expression: [tex]\(30 - (-3y)^3\)[/tex]

- Substitute [tex]\(y = 1\)[/tex].
- Compute [tex]\(30 - (-3(1))^3 = 30 - (-3)^3 = 30 - (-27) = 30 + 27 = 57\)[/tex].

Result: [tex]\(57\)[/tex]

10. Expression: [tex]\(31 [-2(-2a^3)]^3\)[/tex]

- Substitute [tex]\(a = 1\)[/tex].
- Compute [tex]\(31 [-2(-2(1)^3)]^3 = 31 [-2(-2 \cdot 1)]^3 = 31 [-2(-2)]^3 = 31 [4]^3 = 31 \cdot 64 = 64\)[/tex].

Result: [tex]\(64\)[/tex]

So, the results are:

1. [tex]\(2\)[/tex]
2. [tex]\(8\)[/tex]
3. [tex]\(16\)[/tex]
4. [tex]\(135\)[/tex]
5. [tex]\(18\)[/tex]
6. [tex]\(29\)[/tex]
7. [tex]\(-12\)[/tex]
8. [tex]\(8\)[/tex]
9. [tex]\(57\)[/tex]
10. [tex]\(64\)[/tex]

And these computations yield the final results we obtained earlier:
[tex]\[(2, 8, 16, 135, 18, 29, -12, 8, 57, 64).\][/tex]