which expression is equivalent to $left\frac{125^{2}}{125^{\frac{4}{3}}}\right$?\n$\frac{1}{25}$\n$\frac{1}{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: Use exponent - division rule
According to the rule $\frac{a^m}{a^n}=a^{m - n}$, for $\frac{125^2}{125^{\frac{4}{3}}}$, we have $125^{2-\frac{4}{3}}$.
Step2: Calculate the exponent
$2-\frac{4}{3}=\frac{6 - 4}{3}=\frac{2}{3}$, so the expression becomes $125^{\frac{2}{3}}$.
Step3: Rewrite 125
Since $125 = 5^3$, then $125^{\frac{2}{3}}=(5^3)^{\frac{2}{3}}$.
Step4: Use power - of - a - power rule
According to the rule $(a^m)^n=a^{mn}$, $(5^3)^{\frac{2}{3}}=5^{3\times\frac{2}{3}}$.
Step5: Calculate the final result
$5^{3\times\frac{2}{3}} = 5^2=25$.
Answer:
25