Question

b
${ {(3}^{2)} }^{2} - (( - { {2)}^{3)} }^{2} - ( - ( { {5}^{2)} }^{2)}$
​

Answer 1

$\huge\bf{\red{\underline{Question:-}}}$

${ {(3}^{2)} }^{2} - (( - { {2)}^{3)} }^{2} - ( - ( { {5}^{2)} }^{2)}$

$\huge\bf{\underline{Solution:-}}$

$\sf {(a{}^{b})}^{c}=a{}^{b×c}$

Then According to question:-

$\sf {((3){}^{2})}^{2} - {((-2){}^{3})</p><p>}^{2} -{(-5){}^{2})}^{2}$

$\sf (3){}^{2×2}-(-2){}^{3×2}-(-5){}^{2×2}\\ \sf\implies (3){}^{4}-(-2){}^/{6}-(-5){}^{4}\\ \sf\implies 3×3×3×3-(-2)×(-2)×(-2)×(-2)×(-2)×(-2)-(-5)×(-5)×(-5)×(-5)\\ \sf\implies 81- 64-625\\ \sf\implies 81-689\\ \sf\implies (-608)$

$\boxed{\boxed{\pink{(-608)}}}$

$\bf{\underline{Some\: important\: formula\: related\: exponent:-}}$

Let a>0,b>0 Be a real number and let m and n be a rational number.Then :-

$\rm 1) a{}^{m}×a{}^{n}=a{}^{m+n}\\ \rm 2) a{}^{m}×b{}^{m}=(a×b){}^{m}\\ \rm 3){(a{}^{m})}^{n}=a{}^{mn}\\ \rm 4)(ab){}^{m}=a{}^{m}b{}^{m}\\ \rm 5) a{}^{-n}=\frac{1}{a{}^{n}}\\ \rm6)(\frac{a}{b}){}^{m}=\frac{a{}^{m}}{b{}^{m}}\\ \rm 7) \frac{a{}^{m}}{a{}^{n}}=a{}^{m-n}\\ \rm 8 )a{}^{0}=1$