Question

A. -11/3

B. -7/3

C. 7/3

D. 11/3

Answer 1

Answer:

$\displaystyle a = \frac{-11}{3}$

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]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 9 = (\frac{1}{27})^{a + 3}$

Step 2: Solve for a

1. Rewrite:                                                                                                             $\displaystyle 3^2 = (\frac{1}{27})^{a + 3}$
2. Rewrite:                                                                                                             $\displaystyle 3^2 = (\frac{1}{3^3})^{a + 3}$
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:                                $\displaystyle \frac{-2}{3} = a + 3$
7. [Subtraction Property of Equality] Subtract 3 on both sides:                        $\displaystyle \frac{-11}{3} = a$
8. Rewrite:                                                                                                             $\displaystyle a = \frac{-11}{3}$