Question

simplify and express each of the following in exponential form
$\frac{2 {}^{8} \times a {}^{5} }{4 {}^{3} \times a {}^{3} }$
$\frac{3 \times 7 {}^{2} \times 11 {}^{8} }{21 \times 11 {}^{3} }$
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Answer 1

Answer:

To Simplify :-

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

$\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}}$

Solution:-

1) $\sf \frac{2^{8}\times a^{5}}{4^{3}\times a^{3}}$

We know that,

$\sf 4^{3} can\: also\: be\: written\:as\: (2^{2})^{3}$

= $\sf (2)^{2\times3}$

= $\sf 2^{6}$

1) $\sf \frac{2^{8}\times a^{5}}{4^{3}\times a^{3}}$

= $\sf \dfrac{2^{8}\times a^{5}}{2^{6}\times a^{3}}$

= $\sf 2^{8 - 6}\times a^{5 - 3}$

[Since , $\sf\dfrac{b^{m}}{b^{n}} = b^{m - n}$]

= $\sf 2^{2}\times a^{2}$

= $\sf 4\times a^{2}$

= $\sf 4a^{2}$

$\sf\therefore\frac{2^{8}\times a^{5}}{4^{3}\times a^{3}} = 4a^{2}$

2) $\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}}$

= $\sf\dfrac{3\times 7^{2}\times 11^{8}}{3\times 7\times 11^{3}}$

[Since, 21 = 3$\sf\times$ 7]

= $\sf\dfrac{\not{3}\times 7^{2}\times 11^{8}}{\not{3}\times 7\times 11^{3}}$

= $\sf 7^{2 - 1}\times 11^{8 - 3}$

[Since , $\sf\dfrac{b^{m}}{b^{n}} = b^{m - n}$]

= $\sf 7^{1}\times 11^{5}$

= $\sf 7\times 161051$

= 1127357

$\sf\therefore\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}} = 1127357$