Question

map 4c1
unit 6 quiz: exponential expressions
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1. write each of the following as a single power. then evaluate

(a) $3^3 \times 3^4$
(b) $\frac{5^{10}}{5^4}$ (2 mks.)
(c) $\frac{(-8)^3 \times (-8)^5}{(-8)^9}$
(d) $\frac{(2^2)^8 \times 2^0}{(2^3)^4}$ (4 mks.)

1. simplify each to a power that has positive exponents only. then evaluate.

(a) $7^{-4}$
(b) $(-12)^{-3}$ (4 mks.)
(over..)
unit 6 quiz

Explanation:

Part 1(a): \( 3^3 \times 3^4 \)

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

\( 3^3 \times 3^4 = 3^{3 + 4} \)

Step2: Simplify the exponent

\( 3^{3 + 4} = 3^7 \)

Step3: Evaluate \( 3^7 \)

\( 3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187 \)

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

\( \frac{5^{10}}{5^4} = 5^{10 - 4} \)

Step2: Simplify the exponent

\( 5^{10 - 4} = 5^6 \)

Step3: Evaluate \( 5^6 \)

\( 5^6 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625 \)

Step1: Apply product rule to numerator (\(a^m \times a^n = a^{m + n}\))

\( (-8)^3 \times (-8)^5 = (-8)^{3 + 5} = (-8)^8 \)

Step2: Apply quotient rule (\( \frac{a^m}{a^n} = a^{m - n} \))

\( \frac{(-8)^8}{(-8)^7} = (-8)^{8 - 7} \)

Step3: Simplify the exponent

\( (-8)^{8 - 7} = (-8)^1 = -8 \)

Answer:

Single power is \( 3^7 \), value is \( 2187 \)

Part 1(b): \( \frac{5^{10}}{5^4} \)