I can help you solve the problems from the worksheet you provided. Let's start with the first section and work through it step by step.

1. Evaluate the below expressions:

Problem 1:

$(3^3 \cdot 2^2)^2$

• First, simplify inside the parentheses:

  • $3^3 = 27$
  • $2^2 = 4$
  • So, $27 \cdot 4 = 108$

• Now raise $108$ to the power of 2: $108^2 = 11,664$

So, the solution is $11,664$.

Problem 2:

$\left( \frac{-2}{5} \right)^3 \cdot \left( \frac{2}{3} \right)^2$

• First, calculate the powers separately:

  • $\left( \frac{-2}{5} \right)^3 = \frac{(-2)^3}{5^3} = \frac{-8}{125}$
  • $\left( \frac{2}{3} \right)^2 = \frac{2^2}{3^2} = \frac{4}{9}$

• Multiply the two fractions: $\frac{-8}{125} \cdot \frac{4}{9} = \frac{-8 \cdot 4}{125 \cdot 9} = \frac{-32}{1125}$

So, the solution is $\frac{-32}{1125}$.

Problem 3:

$(-3)^0 \cdot (-4)^{-2}$

• $(-3)^0 = 1$ (Any number to the power of 0 is 1)

• $(-4)^{-2} = \frac{1}{(-4)^2} = \frac{1}{16}$

• Multiply: $1 \cdot \frac{1}{16} = \frac{1}{16}$

So, the solution is $\frac{1}{16}$.

Problem 4:

Given