Please help me with my math and explain it to me: 1. \( 3^2 \times 2^3 - (10 - 2) \div 4 \) 2. \( 8\sqrt{16} - 6\sqrt{9} \)

To solve these expressions, we will follow the order of operations, also known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Let's start with the first expression: \( 3^2 \times 2^3 - (10 - 2) \div 4 \)

Step 1: Simplify the parentheses (10 - 2) = 8

Step 2: Evaluate the exponents \( 3^2 = 9 \) and \( 2^3 = 8 \)

Step 3: Perform the multiplication \( 9 \times 8 = 72 \)

Step 4: Perform the division using the result from Step 1, \( 8 \div 4 = 2 \)

Step 5: Perform the subtraction, \( 72 - 2 = 70 \)

So, the final answer is: \( 70 \)

Now, let's solve the second expression: \( 8\sqrt{16} - 6\sqrt{9} \)

Step 1: Calculate the square roots, \( \sqrt{16} = 4 \) and \( \sqrt{9} = 3 \)

Step 2: Multiply the coefficients by their respective square roots, \( 8 \times 4 = 32 \) and \( 6 \times 3 = 18 \)

Step 3: Subtract the second product from the first, \( 32 - 18 = 14 \)

So, the final answer is: \( 14 \)

Extra: Exponents are a way to express repeated multiplication of the same number. For example, \( 3^2 \) means \( 3 \times 3 \), which equals 9.

The square root of a number, denoted as \( \sqrt{ } \), is a value that, when multiplied by itself, gives the number inside the root. For example, \( \sqrt{16} = 4 \) because \( 4 \times 4 = 16 \).

Multiplication and Division are done from left to right, just as they appear in the equation.

Subtraction and addition are also done from left to right, following the order in which they appear in the equation.

For these calculations, always make sure that you follow PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction in this order, and remember that within multiplication and division, as well as addition and subtraction, you proceed from left to right.