Negative exponents in denominators can be evaluated using 1b

Negative exponents in denominators can be evaluated using (1/b^-n)=_____, b0. Illustrate this rule with numbers for b and n. Then, use the rule to determine if the following are true or false.

a. 152 = 5²
b. 1(5)2 =

Solution

Whenever we have a negative exponent in denominator then in order to eliminate the negative exponent we need to flip it to the numbertaor. Hence

(1/b^-n) = b^n

a) 1^-5^-2 = 1/ (1^-5)^2 = 1/1^-10 = 1^10 = 1 Hence False

b) 1 (-5) ^-2 = = 1/5^2 = 1/25