Question

please solve this simplify question ​

Answer 1

Answer:

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Answer 2

QUESTION-:

Find the value of -:

$\bf\; (\frac{3}{5})^3\times(\frac{3}{5})^{-2}\times[(\frac{1}{2})^2]^{-2}\times\frac{1}{24}$

EXPLANATION-:

First we will simply the first 2 terms of the expression-:

$\rightarrow \bf\; (\frac{3}{5})^3\times(\frac{3}{5})^{-2}$

Using the law of exponent-:

$\boxed{\bf\;(a)^m\times (a)^n=a^{(m+n)}}$

$\rightarrow \bf\; (\frac{3}{5})^3\times(\frac{3}{5})^{-2}\\\\\rightarrow \bf\;\ (\frac{3}{5})^{3+(-1)}\\\\\rightarrow \bf\; (\frac{3}{5})^2$

So the first 2 terms have been simplified-:

$\bf\; (\frac{3}{5})^2\times[(\frac{1}{2})^2]^{-2}\times\frac{1}{24}$

Now using the law of exponents-:

$\boxed{\bf\; (\frac{a}{b})^n=\frac{a^n}{b^n}}$

Simplifying the 2nd term-:

$\rightarrow \bf\; [(\frac{1}{2})^2]^{-2}\\\\\rightarrow \bf\;[(\frac{1^2}{2^2}}]^{-2}\\\\\rightarrow \bf\; (\frac{1}{4})^{-2}\\\\\rightarrow \bf\; \frac{4^2}{1}\\\\\rightarrow \bf\;16$

Now -:

$\rightarrow \bf\;16\times\frac{1}{24}\\\\\rightarrow \frac{2}{3}$

Now,

$\rightarrow (\frac{3}{5})^2\times \frac{2}{3}\\\\\rightarrow \frac{9}{25}\times\frac{2}{3}\\\\\rightarrow \frac{3}{25}\times2\\\\\rightarrow \boxed{\bf\;\frac{6}{25}}$

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