Expression 1 (E1)
[tex]6 \times 7 - {3}^{2 \times 9} + {4}^{3} [/tex]
Let's Simplify E1
[tex]42- {3}^{18} + 64 \\ 42 - 38742089 + 64 \\ = - 387420383[/tex]
E1, is just simply combining like terms. Plus an expression in math, is simply something that doesn't equal anything, moreover a phrase.
Expression 2 (E2)
[tex]5 + 4 \times 2 + 6 - 2 \times 2 - 1[/tex]
Without Parenthesis, the expression's value is
[tex]5 + 4 \times 2 + 6 - 2 \times 2 - 1 \\ 5 + 8 + 6 - 4 - 1 \\ 13 + 6 - 4 - 1 \\ 19 - 4 - 1 \\ 14[/tex]
With Parentheses, you'll get
[tex]5 + 4 \times 2 + 6 - 2 \times 2 - 1 \\ (5 + 4 )\times 2+ 6 -2 \times 2- 1 \\ ((9) \times 2) + 6 - 2 \times 2 - 1 \\ (18) + 6 - 2 \times 2 - 1 \\ (24) - 2 \times 2 - 1 \\ (24) - 4 - 1 \\ 19[/tex]
In E2, you expression first has a value of 14 due to the order of operations, PEMDAS (Please Excuse My Dear Aunt Sally) standing for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. When using the order operations before the parentheses, multiplication is done first before 5 is added to 4, order states that 4 must be multiplied by 2 first before addition. However, when placing a parentheses around 5 plus 4 we are now multiplying the value of that expression, (5+4), by 2, so it becomes 9×2, because the order of operations must be followed.
