Question

${\frac{ {25 \times}{5}^{6} \times {7}^{9}}{{5}^{5} \times {7}^{5}}}$
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Answer 1

➤ Answer :-

${\tt \longrightarrow \dfrac{25 \times {5}^{6} \times {7}^{9}}{ {5}^{5} \times {7}^{5}}}$

Write all the numbers in the base and exponential format.........

$\tt \longrightarrow \dfrac{{5}^{2} \times {5}^{6} \times {7}^{9}}{{5}^{5} \times {7}^{5}}$

The formulas to be used here are :-

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

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

Now, solving the problem............

${\tt \longrightarrow \dfrac{{5}^{2 + 6} \times {7}^{9}}{ {5}^{5} \times {7}^{5}}}$

${\tt \longrightarrow \dfrac{{5}^{8} \times {7}^{9}}{{5}^{5} \times {7}^{5}}}$

Here, we should use the second formula given at top.........

${\tt \longrightarrow ({5}^{8 - 5}) \times ({7}^{9 - 5}) = {5}^{3} \times {7}^{4}}$

${\tt \longrightarrow (5 \times 5 \times 5) \times (7 \times 7 \times 7 \times 7)}$

$\tt \longrightarrow 125 \times 2401$

$\tt \longrightarrow 300125$

$\Huge\therefore$The answer for the given problem is 300125.

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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 :-

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

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

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

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