Question

question 19
simplify:
(5n⁻⁴)³
options:
125/n¹²
1/(15n⁶⁴)
15/n¹²
1/(125n⁶⁴)
question 20
find the expression that is equivalent to (b - 4)(b - 6).
options:
b² - 10b - 24
b² - 10b + 24
b² - 2b + 24
b² - 2b - 24

Explanation:

Question 19

Step1: Apply power of a product rule

$(ab)^c = a^c b^c$
$\implies 5^3 \cdot (n^{-4})^3$

Step2: Calculate constant and exponent rule

$(a^m)^n = a^{m \cdot n}$
$\implies 125 \cdot n^{-12}$

Step3: Rewrite negative exponent

$a^{-m} = \frac{1}{a^m}$
$\implies \frac{125}{n^{12}}$

Step1: Apply FOIL method

First, Outer, Inner, Last
$\implies b \cdot b + b \cdot (-6) + (-4) \cdot b + (-4) \cdot (-6)$

Step2: Simplify each term

Calculate products
$\implies b^2 -6b -4b +24$

Step3: Combine like terms

Add linear terms
$\implies b^2 -10b +24$

Answer:

$\frac{125}{n^{12}}$

---

Question 20