Solve the following problems. S(2+7^2)+6^3+2S(4-3)+2^2-17+5=underline ( ) a. What is the answer cubed? 4times 6-4+2+vert 17-9vert times 2vert 14+8-2vert times 10+5=underline ( ) a. What is the answer squared? __ 58. Find the GCF for the following numbers: 108 , 72,63 , 54,45 ,36,27 and 18 59. Find the LCM for the following numbers: 24,36,48,72,90,336 and 480 60. 3-vert -2vert +vert -4vert +15-7+vert -25vert -vert -35vert +14-2vert 3+6vert +5vert -3+6vert = a. What is the answer squared? __ b. What is the answer cubed? __ c.What is the answer to the 5th power? __

## Step 1: Evaluating the first expression<br />### We follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).<br />$S$ likely represents multiplication, so $2S(4-3)$ is $2\times(4-3)$.<br />$2 + 7^2 = 2 + 49 = 51$.<br />$6^3 = 216$.<br />$2 \times (4-3) = 2 \times 1 = 2$.<br />$2^2 = 4$.<br />So, the expression becomes $51 + 216 + 2 + 4 - 17 + 5 = 251$.<br />Cubing the result: $251^3 = 15813251$.<br /><br />## Step 2: Evaluating the second expression<br />### Again, we follow the order of operations.<br />$4 \times 6 - 4 + 2 = 24 - 4 + 2 = 22$.<br />$|17 - 9| = |8| = 8$.<br />$|14 + 8 - 2| = |20| = 20$.<br />So, the expression becomes $22 + 8 \times 2 \times 20 \times 10 + 5 = 22 + 3200 + 5 = 3227$.<br />Squaring the result: $3227^2 = 10413529$.<br /><br />## Step 3: Finding the GCF of the given numbers<br />### We list the factors of each number and find the greatest common factor.<br />Factors of 10872: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 45, 54, 72, 108, 151, 302, 453, 604, 906, 1208, 1359, 1812, 2718, 3624, 5436, 10872<br />Factors of 63: 1, 3, 7, 9, 21, 63<br />Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54<br />Factors of 45: 1, 3, 5, 9, 15, 45<br />Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36<br />Factors of 27: 1, 3, 9, 27<br />Factors of 18: 1, 2, 3, 6, 9, 18<br />The GCF is 9.<br /><br />## Step 4: Finding the LCM of the given numbers<br />### We list the multiples of each number and find the least common multiple.<br />Using prime factorization and taking the highest power of each prime factor, the LCM of 24, 36, 48, 72, 90, 336, and 480 is 10080.<br /><br />## Step 5: Evaluating the third expression<br />### We evaluate the expression using the order of operations and the definition of absolute value.<br />$3 - |-2| + |-4| + 15 - 7 + |-25| - |-35| + 14 - 2|3+6| + 5|-3+6| = 3 - 2 + 4 + 15 - 7 + 25 - 35 + 14 - 2|9| + 5|3| = 3 - 2 + 4 + 15 - 7 + 25 - 35 + 14 - 18 + 15 = 25$.<br />$25^2 = 625$.<br />$25^3 = 15625$.<br />$25^5 = 9765625$.