Question

Simplify 2*3^4*2^5/9*4^2

Answer 1

$\dfrac{2\times 3^{4}\times 2^{5}}{9\times 4^{2}}=36$

Tips :

If $a,b$ are real numbers and $m,n$ are rational numbers, then we have some formulae:

• $a^{1}=a$

• $(a^{m})^{n}=a^{mn}$

• $a^{m}\times a^{n}=a^{m+n}$

• $\dfrac{a^{m}}{a^{n}}=a^{m-n}$

Step-by-step explanation:

Now, $\dfrac{2\times 3^{4}\times 2^{5}}{9\times 4^{2}}$

$=\dfrac{2^{1}\times 3^{4}\times 2^{5}}{3^{2}\times (2^{2})^{2}}$

• Used: $a^{1}=a$

$=\dfrac{2^{1}\times 2^{5}\times 3^{4}}{3^{2}\times 2^{4}}$

• Used: $(a^{m})^{n}=a^{mn}$

$=\dfrac{2^{1+5}\times 3^{4}}{2^{4}\times 3^{2}}$

• Used: $a^{m}\times a^{n}=a^{m+n}$

$=\dfrac{2^{6}\times 3^{4}}{2^{4}\times 3^{2}}$

$=2^{6-4}\times 3^{4-2}$

• Used: $\dfrac{a^{m}}{a^{n}}=a^{m-n}$

$=2^{2}\times 3^{2}$

$=4\times 9$

$=36$

Answer 2

Step-by-step explanation:

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