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} = a^{n} × b^{n}
Rule 2: (a / b)^{n} = a^{n} / b^{n}
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 References and Links
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
Home Page