Question

help no pranksplease​

Answer 1

Solution :

$\displaystyle \bigg(\frac{3^{-1}\times 5^{-2}}{3^{2}\times 5^{-4}}\bigg)^{1/3}\times \bigg(\frac{3^{-1}\times 5^{-1}}{3^{3}\times 5^{-5}}\bigg)^{-1/2}$

$\displaystyle=\bigg(\frac{5^{-2}\times 5^{4}}{3^{2}\times 3^{1}}\bigg)^{1/3}\times \bigg(\frac{5^{-1}\times 5^{5}}{3^{3}\times 3^{1}}\bigg)^{-1/2}$

$\displaystyle=\bigg(\frac{5^{-2+4}}{3^{2+1}}\bigg)^{1/3}\times \bigg(\frac{5^{-1+5}}{3^{3+1}}\bigg)^{-1/2}$

$\displaystyle=\bigg(\frac{5^{2}}{3^{3}}\bigg)^{1/3}\times \bigg(\frac{5^{4}}{3^{4}}\bigg)^{-1/2}$

$\displaystyle=\frac{5^{2/3}}{3^{3/3}}\times \frac{5^{-4/2}}{3^{-4/2}}$

$\displaystyle=\frac{5^{2/3}}{3^{1}}\times \frac{5^{-2}}{3^{-2}}$

$\displaystyle=\frac{3^{2}\times 3^{-1}}{5^{-2/3}\times 5^{2}}$

$\displaystyle=\frac{3^{2-1}}{5^{2-2/3}}$

$\displaystyle=\frac{3^{1}}{5^{4/3}}$

$\to \displaystyle \boxed{\bigg(\frac{3^{-1}\times 5^{-2}}{3^{2}\times 5^{-4}}\bigg)^{1/3}\times \bigg(\frac{3^{-1}\times 5^{-1}}{3^{3}\times 5^{-5}}\bigg)^{-1/2}=\frac{3^{1}}{5^{4/3}}}$

Laws of Indices :

$\displaystyle 1.\:a^{m}\times a^{n}=a^{m+n}$

$\displaystyle 2.\:a^{m}\div a^{n}=a^{m-n}$

$\displaystyle 3.\:(a^{m})^{n/p}=a^{mn/p}$

Answer 2

Hi, your sweet answer is above ;

Formula to be remembered:

$x ^{m } \div x^{n} = x ^{m - n}$

$x ^{m} \times x^{n} = x^{m + n}$

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