map 4c1
unit 6 quiz: exponential expressions
name:
date:
total:
instructions: please provide full, polished solutions for each in the spaces
provided. show all work to guarantee full marks.
1. write each of the following as a single power. then evaluate.
(a) ( 3^3 imes 3^4 )
(b) ( \frac{5^{10}}{5^1} ) (2 mks.)
(c) ( \frac{(-8)^3 imes (-8)^5}{(-8)^7} )
(d) ( \frac{(2^2)^8 imes 2^0}{(2^3)^4} ) (4 mks.)
2. simplify each to a power that has positive exponents only. then evaluate.
(a) ( 7^{-4} )
(b) ( (-12)^{-3} ) (4 mks.)
(over..)
unit 6 quiz

Question

map 4c1
unit 6 quiz: exponential expressions
name:
date:
total:
instructions: please provide full, polished solutions for each in the spaces
provided. show all work to guarantee full marks.
1. write each of the following as a single power. then evaluate.
(a) ( 3^3 	imes 3^4 )
(b) ( \frac{5^{10}}{5^1} ) (2 mks.)
(c) ( \frac{(-8)^3 	imes (-8)^5}{(-8)^7} )
(d) ( \frac{(2^2)^8 	imes 2^0}{(2^3)^4} ) (4 mks.)
2. simplify each to a power that has positive exponents only. then evaluate.
(a) ( 7^{-4} )
(b) ( (-12)^{-3} ) (4 mks.)
(over..)
unit 6 quiz

Accepted Answer

### 1. (a) $ 3^3 \times 3^4 $
# Explanation:
## Step1: Use exponent rule $ a^m \times a^n = a^{m + n} $
$ 3^3 \times 3^4 = 3^{3 + 4} = 3^7 $
## Step2: Evaluate $ 3^7 $
$ 3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187 $
# Answer: Single power is $ 3^7 $, value is $ 2187 $

### 1. (b) $ \frac{5^{10}}{5^1} $ (assuming the denominator is $ 5^1 $ as the handwritten part suggests $ 5^1 $)
# Explanation:
## Step1: Use exponent rule $ \frac{a^m}{a^n} = a^{m - n} $
$ \frac{5^{10}}{5^1} = 5^{10 - 1} = 5^9 $
## Step2: Evaluate $ 5^9 $
$ 5^9 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 1953125 $
# Answer: Single power is $ 5^9 $, value is $ 1953125 $

### 1. (c) $ \frac{(-8)^3 \times (-8)^5}{(-8)^7} $
# Explanation:
## Step1: Use $ a^m \times a^n = a^{m + n} $ in numerator
$ (-8)^3 \times (-8)^5 = (-8)^{3 + 5} = (-8)^8 $
## Step2: Use $ \frac{a^m}{a^n} = a^{m - n} $
$ \frac{(-8)^8}{(-8)^7} = (-8)^{8 - 7} = (-8)^1 = -8 $ (Note: The previous handwritten step had an error, the correct exponent subtraction gives $ 8 - 7 = 1 $, not $ -1 $)
# Answer: Single power is $ (-8)^1 $ (or $ -8 $), value is $ -8 $

### 1. (d) $ \frac{(2^2)^8 \times 2^0}{(2^3)^4} $
# Explanation:
## Step1: Use $ (a^m)^n = a^{m \times n} $
$ (2^2)^8 = 2^{2 \times 8} = 2^{16} $, $ (2^3)^4 = 2^{3 \times 4} = 2^{12} $, and $ 2^0 = 1 $
## Step2: Simplify numerator: $ 2^{16} \times 1 = 2^{16} $
## Step3: Use $ \frac{a^m}{a^n} = a^{m - n} $
$ \frac{2^{16}}{2^{12}} = 2^{16 - 12} = 2^4 $
## Step4: Evaluate $ 2^4 $
$ 2^4 = 16 $
# Answer: Single power is $ 2^4 $, value is $ 16 $

### 2. (a) $ 7^{-4} $
# Explanation:
## Step1: Use negative exponent rule $ a^{-n} = \frac{1}{a^n} $
$ 7^{-4} = \frac{1}{7^4} $
## Step2: Evaluate $ 7^4 = 7 \times 7 \times 7 \times 7 = 2401 $, so $ \frac{1}{7^4} = \frac{1}{2401} \approx 0.0004165 $
# Answer: Positive exponent form is $ \frac{1}{7^4} $, value is $ \frac{1}{2401} $ (or approximately $ 0.0004165 $)

### 2. (b) $ (-12)^{-3} $
# Explanation:
## Step1: Use $ a^{-n} = \frac{1}{a^n} $
$ (-12)^{-3} = \frac{1}{(-12)^3} $
## Step2: Evaluate $ (-12)^3 = -12 \times -12 \times -12 = -1728 $, so $ \frac{1}{(-12)^3} = \frac{1}{-1728} = -\frac{1}{1728} \approx -0.0005787 $
# Answer: Positive exponent form is $ \frac{1}{(-12)^3} $ (or $ -\frac{1}{12^3} $), value is $ -\frac{1}{1728} $

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QUESTION IMAGE

Question

Explanation:

1. (a) \( 3^3 \times 3^4 \)

Step1: Use exponent rule \( a^m \times a^n = a^{m + n} \)

Step2: Evaluate \( 3^7 \)

Step1: Use exponent rule \( \frac{a^m}{a^n} = a^{m - n} \)

Step2: Evaluate \( 5^9 \)

Step1: Use \( a^m \times a^n = a^{m + n} \) in numerator

Step2: Use \( \frac{a^m}{a^n} = a^{m - n} \)

Answer:

1. (b) \( \frac{5^{10}}{5^1} \) (assuming the denominator is \( 5^1 \) as the handwritten part suggests \( 5^1 \))