Question

tele the answer of the question
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Answer 1

Answer:

$\frac{ {5}^{4} \times 49 \times 8 \times 7 }{ {7}^{5} \times {2}^{3} \times 5 } = \frac{ {5}^{3} }{ {7}^{2} }$

Step-by-step explanation:

$\frac{ {5}^{4} \times 49 \times 8 \times 7 }{ {7}^{5} \times {2}^{3} \times 5 } \\ = \frac{5 \times 5 \times 5 \times 5 \times 7 \times 7 \times 2 \times 2 \times 2 \times 7}{7 \times 7 \times 7 \times 7 \times 7 \times 2 \times 2 \times 2 \times 5} \\ = \frac{5 \times 5 \times 5}{7 \times 7 } \\ = \frac{ {5}^{3} }{ {7}^{2} }$

Answer 2

Question :-

$\sf \frac{5^4 \times 49 \times 8 \times 7}{7^5 \times 2^3 \times 5}$

Answer :-

$\implies\sf \frac{5^4 \times 49 \times 8 \times 7}{7^5 \times 2^3 \times 5}$

$\implies\sf \frac{5^4 \times 7^2 \times \cancel{2^3} \times 7}{7^5 \times \cancel{2^3} \times 5}$

$\implies\sf \frac{5^4 \times ( 7^2 \times 7 )}{7^5 \times 5}$

$\implies\sf \frac{5^4 \times 7^3}{7^5 \times 5}$

$\implies\sf \frac{5^{4-1} \times 7^3}{7^5}$

$\implies\sf 5^3 \times 7^{3-5}$

$\implies\sf 5^3 \times 7^{-2}$

$\implies\sf \frac{5^3}{7^2}$

$\implies\boxed{\sf \frac{125}{49}}$

Additional information :-

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$