Question

Simplify answer it's urgent please please I will surely follow you​

Answer 1

➤ Answer :-

${\tt \longrightarrow \dfrac{ {3}^{5} \times {10}^{5} \times 25 }{{5}^{7} \times {6}^{5}}}$

First, we should write all the digits in exponential form......

${\tt \longrightarrow \dfrac{{3}^{5} \times {10}^{5} \times {5}^{2}}{{5}^{7} \times {6}^{5}}}$

${\tt \longrightarrow \dfrac{ {3}^{5} \times (5 \times 2)^{5} \times {5}^{2}}{ {5}^{7} \times (3 \times 2)^{5}}}$

${\tt \longrightarrow \dfrac{{3}^{5} \times {5}^{5} \times {2}^{5} \times {5}^{2}}{{5}^{7} \times {3}^{5} \times {2}^{5}}}$

${\tt \longrightarrow \dfrac{ {3}^{5} \times {5}^{5 + 2} \times {2}^{5}}{{5}^{7} \times {3}^{5} \times {2}^{5}}}$

${\tt \longrightarrow \dfrac{{3}^{5} \times {5}^{7} \times {2}^{5}}{{5}^{7} \times {3}^{5} \times {2}^{5}}}$

Now, simplify each of them by looking into the bases......

${\tt \longrightarrow ({3}^{5 - 5})\times ({5}^{7 - 7}) \times ({2}^{5 - 5})}$

${\tt \longrightarrow {3}^{0} \times {5}^{0} \times {2}^{0}}$

Here, note that any base having a power of 0, tge value will be one.

So,

${\tt \longrightarrow 1 \times 1 \times 1 = \boxed{\tt 1}}$

$\Huge\therefore$The answer is One (1).

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More to know...........

• While solving the problems of exponents and powers, if the given numbers are composite numbers, we should represent in their prime factors. We can also do cancellation, when the base are same.

Laws of exponents :-

${\sf \dashrightarrow {a}^{m} \times {a}^{n} = {a}^{m + n}}$

${\sf \dashrightarrow {a}^{m} \div {a}^{n} = {a}^{m-n}}$

${\sf \dashrightarrow ({a}^{m})^{n} = {a}^{m \times n}}$

${\sf \dashrightarrow {a}^{0} = 1}$