Sure, let’s dive into each of these expressions one by one:
1. [tex]\((2 - 4)^2 - 6\)[/tex]
- First, inside the parentheses: [tex]\(2 - 4 = -2\)[/tex].
- Next, square the result: [tex]\((-2)^2 = 4\)[/tex].
- Finally, subtract 6: [tex]\(4 - 6 = -2\)[/tex].
So, [tex]\((2 - 4)^2 - 6 = -2\)[/tex].
2. [tex]\(9 \cdot 8^2 + 7\)[/tex]
- First, evaluate the exponent: [tex]\(8^2 = 64\)[/tex].
- Next, multiply by 9: [tex]\(9 \cdot 64 = 576\)[/tex].
- Finally, add 7: [tex]\(576 + 7 = 583\)[/tex].
So, [tex]\(9 \cdot 8^2 + 7 = 583\)[/tex].
3. [tex]\((-5)^2 - 6 \cdot (-5) - 8\)[/tex]
- First, evaluate the exponent: [tex]\((-5)^2 = 25\)[/tex].
- Next, multiply: [tex]\(-6 \cdot (-5) = 30\)[/tex].
- Then add the two products: [tex]\(25 + 30 = 55\)[/tex].
- Finally, subtract 8: [tex]\(55 - 8 = 47\)[/tex].
So, [tex]\((-5)^2 - 6(-5) - 8 = 47\)[/tex].
4. [tex]\(6 - 9 \left(8^2 - 7\right) - (-9)\)[/tex]
- First, evaluate the exponent: [tex]\(8^2 = 64\)[/tex].
- Next, inside the parentheses: [tex]\(64 - 7 = 57\)[/tex].
- Then multiply by 9: [tex]\(9 \cdot 57 = 513\)[/tex].
- Now, subtract from 6: [tex]\(6 - 513 = -507\)[/tex].
- Finally, subtract [tex]\(-9\)[/tex]: [tex]\(-507 + 9 = -498\)[/tex].
So, [tex]\(6 - 9 \left(8^2 - 7\right) - (-9) = -498\)[/tex].
5. [tex]\((-6) - (-3) \left(2^3 - (-2)\right)\)[/tex]
- First, evaluate the exponent: [tex]\(2^3 = 8\)[/tex].
- Next, inside the parentheses: [tex]\(8 - (-2) = 10\)[/tex].
- Then multiply by [tex]\(-3\)[/tex]: [tex]\(-3 \cdot 10 = -30\)[/tex].
- Finally, add the negative product to [tex]\(-6\)[/tex]: [tex]\(-6 - (-30) = -6 + 30 = 24\)[/tex].
So, [tex]\((-6) - (-3) \left(2^3 - (-2)\right) = 24\)[/tex].
