Question

(20x⁻³)x) / (4 x⁴)⁻⁵
a) 5x⁻⁴
b) -5x⁻⁴
c) 5x⁻²
d) -5x⁻²

Answer 1

To simplify the given expression, first simplify the expressions inside the parentheses and the second set of parentheses. Then, divide the two expressions, following the rules of exponents. The simplified expression is 20x.

Step-by-step explanation:

To simplify the given expression, we need to use the rules of exponents.

First, let's simplify the expression inside the parentheses: (20x⁻³)x = 20x⁻³x⁻¹ = 20x⁻⁴.

Next, let's simplify the expression inside the second set of parentheses: (4x⁴)⁻⁵ = 4⁻⁵x⁻⁵×⁴⁻⁵ = x⁻⁵.

Finally, let's divide the two expressions: 20x⁻⁴ ÷ x⁻⁵ = 20x⁻⁴⁻⁻(−5) = 20x⁻⁴ × x⁵ = 20x¹ = 20x.

Therefore, the simplified expression is 20x.