Question
p. Simplify each using exponent laws,then evaluate No decimal answers. b) 7^6div 7^2 c) (1/3)^4times (1/3)^-7 d) (4^2)^3
Solution
4.1
(247 Votes)
Garland
Elite · Tutor for 8 years
Answer
**b) 7⁶ ÷ 7²*** **Exponent Law:** When dividing with the same base, subtract the exponents. aᵐ ÷ aⁿ = a^(m-n)* **Application:** 7⁶ ÷ 7² = 7^(6-2) = 7⁴* **Evaluation:** 7⁴ = 7 * 7 * 7 * 7 = 2401**Answer:** 2401**c) (1/3)⁴ × (1/3)⁻⁷*** **Exponent Law:** When multiplying with the same base, add the exponents. aᵐ × aⁿ = a^(m+n)* **Application:** (1/3)⁴ × (1/3)⁻⁷ = (1/3)^(4 + (-7)) = (1/3)⁻³* **Exponent Law:** A negative exponent means reciprocal. a⁻ⁿ = 1/aⁿ* **Application:** (1/3)⁻³ = 1/(1/3)³ = 1/(1/27) = 27**Answer:** 27**d) (4²)³*** **Exponent Law:** When raising a power to a power, multiply the exponents. (aᵐ)ⁿ = a^(m*n)* **Application:** (4²)³ = 4^(2*3) = 4⁶* **Evaluation:** 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 = 4096**Answer:** 4096