Answer:
[tex]\bold{2\frac{14}{25}}[/tex]
Step-by-step explanation:
Follow the PEMDAS order of operations
P = Parenthesis
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Step 1: Parenthesis
The first operation is parenthesis "()", and we have parenthesis so we solve the parenthesis first.
[tex]16\div(2+\frac{1}{2})^2\\\\=\frac{16}{\left(2+\frac{1}{2}\right)^2}[/tex]
[tex]\underline{\mathrm{Solve}}\\\\(2+\frac{1}{2})\\\\=2+\frac{1}{2}\\\\=2\frac{1}{2}[/tex]
[tex]\frac{16}{\left(2\frac{1}{2}\right)^2}[/tex]
Step 2: Exponents
The Exponent is the tiny number on top of a bigger number. For example, we have [tex]2\frac{1}{2}^\bold{2}[/tex], and the bolded part is the exponent. And the number there is how many times you will multiply the bigger number to itself. So we can simplify:
[tex](2\frac{1}{2})^2\\\\=2\frac{1}{2}\times2\frac{1}{2}\\\\=6\frac{1}{4}[/tex]
[tex]\frac{16}{6\frac{1}{4}}[/tex]
Step 3: Division
We don't have any multiplication, so we skip to the next operation in the order. Division:
[tex]\frac{16}{6\frac{1}{4}}=2\frac{14}{25}\\\\\bold{2\frac{14}{25}}[/tex]
