Question

plz answer fast plz find the answer fast plz send me your ans​

Answer 1

❏ Used Formula:-

•From The index formula

(1) $\sf\longrightarrow \frac{X{}^{m}}{X{}^{n}}=X{}^{m-n}\:or\:=\frac{1}{X{}^{n-m}}$

(2) $\sf\longrightarrow X{}^{m}\times X{}^{n}=X{}^{m+n}$

(3) $\sf\longrightarrow X{}^{m}\times Y{}^{m}={XY}^{m}$

(4) $\sf\longrightarrow \frac{X{}^{m}}{Y{}^{m}}=(\frac{X}{Y}){}^{m}$

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❏ Solution:-

Q) • Simplify:-

$\sf\longrightarrow\frac{16\times 2{}^{n+1}-4\times 2{}^{n}}{16\times 2{}^{n+2}-2\times 2{}^{n+2}}=?$

•Ans)

$\sf\longrightarrow\frac{16\times 2{}^{n+1}-4\times 2{}^{n}}{16\times 2{}^{n+2}-2\times 2{}^{n+2}}$

$\sf\longrightarrow\frac{2{}^{4}\times 2{}^{n+1}-2{}^{2}\times 2{}^{n}}{2{}^{4}\times 2{}^{n+2}-2\times 2{}^{n+2}}$

$\sf\longrightarrow\frac{ 2{}^{n+1+4}-2{}^{n+2}}{ 2{}^{n+2+4}- 2{}^{n+2+1}}$

$\sf\longrightarrow\frac{ 2{}^{n+5}-2{}^{n+2}}{ 2{}^{n+6}- 2{}^{n+3}}$

$\sf\longrightarrow \frac{2 {}^{n} \times 2 {}^{5} - 2 {}^{n} \times 2 {}^{2} }{2 {}^{n} \times 2 {}^{6} - 2 {}^{n} \times 2 {}^{3} }$

$\sf\longrightarrow \frac{ \cancel{2 {}^{n}}(2 {}^{5} - 2 {}^{2}) }{ \cancel{2 {}^{n} }(2 {}^{6} - 2 {}^{3} )}$

$\sf\longrightarrow \frac{ (2 {}^{3 + 2} - 2 {}^{2}) }{(2 {}^{3 + 3} - 2 {}^{3}) }$

$\sf\longrightarrow \frac{(2 {}^{3} \times 2 {}^{2} - 2 {}^{2}) }{(2 {}^{3} \times 2 {}^{3} - 2 {}^{3}) }$

$\sf\longrightarrow \frac{2 {}^{2} \cancel{(2 {}^{3} - 1)} }{2 {}^{3} \cancel{(2 {}^{3} - 1)} }$

$\sf\longrightarrow \frac{2 {}^{2} }{2 {}^{3} }$

$\sf\longrightarrow \frac{1}{2 {}^{3-2} }$

$\sf\longrightarrow \frac{1}{2 {}^{1} }$

$\sf\longrightarrow\boxed{ \large{\red{ \frac{1}{2}}} }$

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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