# Free Mathematics Tutorials # Negative Exponents Questions with Detailed Solutions for Grade 8

Detailed solutions and explanations to Grade 8 questions on simplifying expressions with negative exponents .

 Review: Rules of Exponents Rule 1: (a � b)n = an � bn Rule 2: (a / b)n = an / bn Rule 3: a -n = 1 / a n Rule 4: (a / b) -n = (b / a) n Simplify the expression 5 -2 Solution Use rule 3 above to write 5 -2 = 1 / 5 2 = 1 / 25 (-1/3) -2 = Solution Rewrite expression as follows (-1/3) -2 = [ (-1)(1/3) ] -2 Use rule 1 of exponents = (-1) -2 (1/3) -2 Use rules 3 and 4 of negative exponents = [ 1 / (-1) 2 ] [ (3/1) 2 ] = [ 1/1 ] [ 9/1 ] = 9 Simplify the expression (5 -1) / (3 -1) Solution Use rule 2 to rewrite expression as follows (5 -1) / (3 -1) = (5 / 3) -1 Use rule 4 to rewrite expression as follows = (3 / 5) 1 = 3 / 5 (2 -3) � (3 -2) = Solution Use rule 3 to rewrite expression as follows (2 -3) � (3 -2) = (1 / 2 3) � (1 / 3 2) = (1 / 8)(1 / 9) = 1 / 72 Simplify the expression - 2 -3 Solution We first rewrite the given expression as follows - 2 -3 = (-1)(2 -3) We now use rule 3 = (-1)(1 / 2 3) = (-1)(1 / 8) = - 1 / 8 - 1 -3 + 2 -3 = Solution Use rule 3 to rewrite the given expression as follows - 1 -3 + 2 -3 = (-1) (1 / 1 3) + 1 / 2 3 = - 1 / 1 + 1 / 8 = - 1 + 1 / 8 Set fractions to common denominator = - 8 / 8 + 1 / 8 = - 7 / 8 (- 1) -4 + 2 -3 = Solution Use rule 3 to rewrite the given expression as follows (- 1) -4 + 2 -3 = 1 / (-1) 4 + 1 / 2 3 = 1 / 1 + 1 / 8 Set fratcions to common denominator = 8 / 8 + 1 / 8 = 9 / 8 Simplify the expression (- 4 -2)(2 2) Solution Use rule 3 to rewrite the given expression as follows (- 4 -2)(2 2) = - (1 / 4 2 )(2 2) Simplify = - (1 / 16)(4) = - 1 / 4 (- 1) -3 + 2 0 = Solution Note that 2 0 = 1. Use rule 3 to write (- 1) -3 + 2 0 = 1 / (- 1) 3 + 1 Simplify = 1 / (-1) + 1 = -1 + 1 = 0 0 -3 = Solution Use rule 3 to write 0 -3 = 1 / 0 3 = 1 / 0 : division by 0 not allowed and therefore 0 -3 is not a real number.

More Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
More
High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
More
High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
More
Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers