5. Simplify each expression. L21, L22 $$ \begin{array}{ll} ext { a. } \frac{\frac{2}{3}}{\frac{1}{3}}+(16-7) \div 3 & ext { b. } \frac{\sqrt{64}-11 \cdot 3}{-44 \div 4+6^{2}}\end{array} $$

Question

5. Simplify each expression. L21, L22 $$ \begin{array}{ll}	ext { a. } \frac{\frac{2}{3}}{\frac{1}{3}}+(16-7) \div 3 & 	ext { b. } \frac{\sqrt{64}-11 \cdot 3}{-44 \div 4+6^{2}}\end{array} $$

UpStudy AI · Accepted Answer

**a. Simplify**

1. Start with
   $$
   \frac{\frac{2}{3}}{\frac{1}{3}} + (16-7) \div 3
   $$

2. Simplify the complex fraction:
   $$
   \frac{\frac{2}{3}}{\frac{1}{3}} = \frac{2}{3} \times \frac{3}{1} = 2
   $$

3. Compute the subtraction in the parenthesis:
   $$
   16 - 7 = 9
   $$

4. Perform the division:
   $$
   9 \div 3 = 3
   $$

5. Sum the results:
   $$
   2 + 3 = 5
   $$

**b. Simplify**

1. Start with
   $$
   \frac{\sqrt{64} - 11 \cdot 3}{-44 \div 4 + 6^{2}}
   $$

2. Evaluate the square root:
   $$
   \sqrt{64} = 8
   $$

3. Multiply:
   $$
   11 \cdot 3 = 33
   $$

4. Simplify the numerator:
   $$
   8 - 33 = -25
   $$

5. Compute the division in the denominator:
   $$
   -44 \div 4 = -11
   $$

6. Evaluate the exponent:
   $$
   6^2 = 36
   $$

7. Simplify the denominator:
   $$
   -11 + 36 = 25
   $$

8. Form the final fraction:
   $$
   \frac{-25}{25} = -1
   $$

**Final Answers:**

a. $$5$$  
b. $$-1$$
a. 5 b. -1

Simplify each expression. L21, L22

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