which expressions are equivalent to $\frac{10}{10^{\frac{3}{4}}}$?\n$10^{\frac{4}{3}}$\n$10^{\frac{1}{4}}$\n$…

which expressions are equivalent to $\frac{10}{10^{\frac{3}{4}}}$?\n$10^{\frac{4}{3}}$\n$10^{\frac{1}{4}}$\n$sqrt3{10^{4}}$\n$sqrt4{10}$\ndone

which expressions are equivalent to $\frac{10}{10^{\frac{3}{4}}}$?\n$10^{\frac{4}{3}}$\n$10^{\frac{1}{4}}$\n$sqrt3{10^{4}}$\n$sqrt4{10}$\ndone

Answer

Answer:

  1. (10^{\frac{1}{4}})
  2. (\sqrt[4]{10})

Explanation:

Step1: Use exponent - division rule

According to the rule (\frac{a^m}{a^n}=a^{m - n}), for (\frac{10}{10^{\frac{3}{4}}}), where (a = 10), (m=1) and (n=\frac{3}{4}), we have (10^{1-\frac{3}{4}}).

Step2: Calculate the exponent

(1-\frac{3}{4}=\frac{4 - 3}{4}=\frac{1}{4}), so (\frac{10}{10^{\frac{3}{4}}}=10^{\frac{1}{4}}).

Step3: Recall radical - exponent relationship

The fractional - exponent form (a^{\frac{1}{n}}) is equivalent to the radical form (\sqrt[n]{a}). When (a = 10) and (n = 4), (10^{\frac{1}{4}}=\sqrt[4]{10}).