Question

A. -11/3

B. -7/3

C. 7/3

D. 11/3

Answer 1

`\displaystyle a = (-11)/(3)`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Exponential Rule [Powering]:
  `\displaystyle (b^m)^n = b^(m \cdot n)`
• Exponential Rule [Rewrite]:
  `\displaystyle b^(-m) = (1)/(b^m)`

Explanation:

Step 1: Define

Identify

`\displaystyle 9 = ((1)/(27))^(a + 3)`

Step 2: Solve for a

1. Rewrite:
   `\displaystyle 3^2 = ((1)/(27))^(a + 3)`
2. Rewrite:
   `\displaystyle 3^2 = ((1)/(3^3))^(a + 3)`
3. Rewrite [Exponential Rule - Rewrite]:
   `\displaystyle 3^2 = (3^(-3))^(a + 3)`
4. Exponential Rule [Powering]:
   `\displaystyle 3^2 = 3^(-3(a + 3))`
5. Set up:
   `\displaystyle 2 = -3(a + 3)`
6. [Division Property of Equality] Divide -3 on both sides:
   `\displaystyle (-2)/(3) = a + 3`
7. [Subtraction Property of Equality] Subtract 3 on both sides:
   `\displaystyle (-11)/(3) = a`
8. Rewrite:
   `\displaystyle a = (-11)/(3)`