MATH SOLVE

5 months ago

Q:
# Simplify 27 to the negative 2 thirds power. 9 1 over 9 negative 1 over 9 β9

Accepted Solution

A:

Answer:The answer is 1/9 β the second answerStep-by-step explanation:* In the exponential functions we have some rules(1) b^(-m) = 1/(b^m) Β (for all nonzero real numbers b) - If we have negative power we reciprocal the base Β to get positive power(2) (b^m)^n = b^(mn) - If we have power over power we multiply them* In our problem: [tex](27)^{-\frac{2}{3}}[/tex]- At first change 27 to b^nβ΅ 27 = 3 Γ 3 Γ 3 = 3Β³β΄ [tex]27^{-\frac{2}{3}}=(3^{3})^{-\frac{2}{3}}[/tex]* Lets use rule (2)β΄ [tex]27^{-\frac{2}{3}}=3^{-2}[/tex] β 3 Γ -2/3 = -2* Use rule (1)β΄ [tex]3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}[/tex] β reciprocal the fraction to change the sig of the power* The answer is 1/9