Simplify the following exponent numbers by using (a/b)^m = (a^m/b^m) (i) 5^3 ÷ 2^3 (ii) (-2)^4 ÷ 3^4 (iii) 8^6 ÷ 5^6

Question

Simplify the following exponent numbers by using \((\frac{a}{b})^m\) = \(\frac{a^m}{b^m}\)

(i) 5³ ÷ 2³

(ii) (-2)⁴ ÷ 3⁴

(iii) 8⁶ ÷ 5⁶

(iv) 6³ ÷ (-7)³

Answer 1

(i) 5³ ÷ 2³ = (\(\frac{5}{2}\))³ 

[Since \(\frac{a^m}{b^m}\) = (\(\frac{a}{b}\))^m]

(ii) (-2)⁴ ÷ 3⁴ = (\(\frac{-2}{3}\))⁴

(iii) 8⁶ ÷ 5⁶ = (\(\frac{8}{5}\))⁶

(iv) 6³ ÷ (-7)³ = (\(\frac{6}{-7}\))³