Question

describe the three mistakes he made. ((20x)/(5x^(8)))^(-3)=((20x)^(-3))/((5x^(8))^(-3))=((5x^(8))^(3))/((20x)^(3))=(5x^(24))/(20x^(4))=(x^(6))/(4)

Answer 1

The three mistakes made in simplifying the expression are inverting the expression, incorrectly multiplying the exponents, and reducing the expression incorrectly. To correct these mistakes, use the exponent rules for fractions, multiplication, and division.

Step-by-step explanation:

To simplify the expression ((20x)/(5x8))-3, the student made three mistakes:

1. The student incorrectly inverted the expression, resulting in ((5x8)3)/((20x)3) instead of ((20x)-3)/((5x8)-3).
2. The student mistakenly multiplied the exponents when simplifying ((5x8)3) and ((20x)3), resulting in (5x24)/(20x4) instead of (5x24)/(20x-3).
3. Lastly, the student reduced (20x-3) to (x6)/4, which is incorrect. It should be (1/x3)/(20/1), or simply 1/(20x3).

To correct these mistakes, you can use the exponent rules:

1. When raising a fraction to a negative exponent, invert the fraction and make the exponent positive. For example, (a/b)-n = (b/a)n.
2. To multiply exponents with the same base, add the exponents. For example, (am)(an) = am+n.
3. To divide exponents with the same base, subtract the exponents. For example, (am)/(an) = am-n.