Question

SIMPLIFY AND EXPRESS THE RESULT IN THE SIMPLEST FORM ...




can u plz give me answer with attachment thanking:-)​

Answer 1

Solution :-

First of all we should know about the factors of the given numbers :-

25 = 5 × 5 = 5²

243 = 3 × 3 × 3 × 3 × 3 = 3⁵

16 = 2 × 2 × 2 × 2 = 2⁴

8 = 2 × 2 × 2 = 2³

Now we should also know these :-

$x^a = x \times x \times x ...\sf{(upto\: a\: times)}$

$x^{\frac{1}{b}} = \sqrt[b]{x}$

${x}^{\frac{a}{b}} = (\sqrt[b]{x})^a$

Now solving the question :-

$\dfrac{ (25)^{3/2} \times (243)^{2/5}}{ (16)^{5/4} \times (8)^{4/3}}$

$= \dfrac{ (\sqrt[2]{25})^3 \times (\sqrt[5]{243})^2 }{(\sqrt[4]{16})^5 \times (\sqrt[3]{8})^4 }$

$= \dfrac{(\sqrt[2]{5^2})^3 \times (\sqrt[5]{3^5})^2 }{(\sqrt[4]{2^4})^5 \times (\sqrt[3]{2^3})^4 }$

$=\dfrac{5^3 \times 3^2 }{2^5 \times 2^4 }$

$= \dfrac{ 125 \times 9 }{32 \times 16}$

$=\dfrac{ 1125}{512}$

Answer 2

Step-by-step explanation:

Express the result in simplest form: