which expression is equivalent to $left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)$?\n$\frac{1}{25}$\n$\frac{1}…
which expression is equivalent to $left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)$?\n$\frac{1}{25}$\n$\frac{1}{10}$\n$10$\n$25$
Answer
Explanation:
Step1: Rewrite 125 as 5³
Since (125 = 5^3), then (125^2=(5^3)^2) and (125^{\frac{4}{3}}=(5^3)^{\frac{4}{3}}). According to the power - of - a - power rule ((a^m)^n=a^{mn}), ((5^3)^2 = 5^{3\times2}=5^6) and ((5^3)^{\frac{4}{3}}=5^{3\times\frac{4}{3}} = 5^4).
Step2: Simplify the fraction
The original expression (\frac{125^2}{125^{\frac{4}{3}}}) becomes (\frac{5^6}{5^4}). According to the quotient rule of exponents (\frac{a^m}{a^n}=a^{m - n}), so (\frac{5^6}{5^4}=5^{6 - 4}=5^2).
Step3: Calculate the result
(5^2 = 25).
Answer:
25