Question

tell me fast please please​

Answer 1

Step-by-step explanation:

ANSWER:-

$\dfrac{49 \times {7}^{3} \times 100}{ {10}^{3} \times {3}^{3} \times {7}^{2} }$

$= \dfrac{ {7}^{2} \times {7}^{3} \times {10}^{2} }{ {10}^{3} \times {3}^{3} \times {7}^{2} }$

$\dfrac{ {7}^{(2 + 3)} \times {10}^{2} }{ {10}^{3} \times {3}^{3} \times {7}^{2} }$

$\dfrac{ {7}^{(2 + 3 - 2)} \times {10}^{(2 - 3)} }{ {3}^{3} }$

$= \dfrac{343}{270}$

(ii)

$\dfrac{121 \times {5}^{3} }{ {11}^{2} \times 5}$

$\frac{ {11}^{2} \times {5}^{3} }{ {11}^{2} \times 5 }$

$= {5}^{2} = 25$

(iii)

$\dfrac{ {a}^{3} \times {b}^{2} \times {b}^{3} \times {a}^{2} }{ {a}^{2} \times b }$

${a}^{3} \times {b}^{(2 + 3 - 1)}$

$= {a}^{3} \times {b}^{4}$

(iv)

$\dfrac{ {2}^{8} \times {4}^{2} \times {5}^{3} }{16 \times {10}^{2} }$

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

$2^{(8+4-(4+2)} \times 5^{(3-2)}$

$2^6 \times 5$

= 320

Things to Note:-

• Always when you see any exponent, then when it is divided, with same bases, the powers get subtracted.
• Always when same bases get multiply. power adds.

Answer 2

a)

$\sf\frac{49 \times{7}^{3} \times 100 }{{10}^{3} \times {3}^{3} \times {7}^{2} }$

$= \sf\frac{\cancel{49} \times 343 \times 1\cancel{00}}{10\cancel{00} \times 27 \times \cancel{49}}$

$=\sf \frac{343}{270}$

b)

$\sf \frac{121 \times {5}^{3} }{ {11}^{2} \times 5 }$

$=\sf \frac{\cancel{121} \times\cancel{ {125}}^{25}}{\cancel{121} \times \cancel{5}}$

$= \sf25$

c)

$\sf \frac{ {a}^{3} \times {b}^{2} \times {b}^{3} \times {a}^{2} }{ {a}^{2} \times b }$

$=\sf \frac{ {a}^{3} \times \cancel{ {b}^{2}}^b \times {b}^{3} \times \cancel{{a}^{2}} }{\cancel{ {a}^{2}} \times \cancel{b} }$

$=\sf {a}^{3} \times {b}^{(3 + 1)}$

$=\sf {a}^{3} \times {b}^{4}$

$=\sf {a}^{3} {b}^{4}$

d)

$\sf \frac{ {2}^{8} \times {4}^{2} \times {5}^{3} }{16 \times {10}^{2} }$

$=\sf \frac{\cancel{256}^{64} \times \cancel{16} \times \cancel{125}^{\cancel{25}^{5}}}{\cancel{16} \times \cancel{100}^{\cancel{20}^{\cancel{4}}}}$

$=\sf 320$