Question

8. (i) (ii) and 9. (i) pls answer with explanation​

Answer 1

✰Solution :

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• 8. Simplify -

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$\large\rm \: i) \: \: \: \mathtt{ \dfrac{{( {2}^{5}) }^{2} \times {7}^{3} }{ {8}^{3} \times 7} }$

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☞︎︎︎ Powers power = power multiply

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☞︎︎︎ 7³ ÷ 7 = 7²

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$\large \implies \: \: \mathtt{ \dfrac{{( {2}^{}) }^{10} \times {7}^{ \cancel 3 \: 2} \: \: \: }{ {8}^{3} \times \cancel 7} }$

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$\large \implies \: \: \mathtt{ \dfrac{{{1024}^{}}^{} \times {49}^{ } \: \: \: }{ {512}^{} } } \\ \\ \\ \\ \implies \: \large \mathtt{ \dfrac{{{ \cancel{1024} \: \: 2}^{}}^{} \times {49}^{ } \: \: \: }{ { \cancel{512}}^{} } }$

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$\large \implies \: 2 \times 49 = \boxed{98}$

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$\large \rm \: ii) \: \: \mathtt{\dfrac{25 \times {5}^{2} \times {t}^{8} }{ {10}^{3} \times {t}^{4} } }$

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• t⁸ ÷ t⁴ = (in division when bases are same powers are subtracted)

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• t⁸ ÷ t⁴ = 8 - 4 = t⁴

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$\large \implies \: \mathtt{\dfrac{25 \times {5}^{2} \times {t}^{ \cancel8 \: 4} }{ {10}^{3} \times {t}^{ \cancel4} } }$

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$\large \implies \: \mathtt{\dfrac{25 \times {25} \times {t}^{ 4} }{ {1000 } }} \\ \\ \\ \large \implies \: \mathtt{\dfrac{ \cancel{25} \times {25} \times {t}^{ 4} }{ { \cancel{1000 }} \: \: 40 }}$

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$\large \implies \mathtt{ \dfrac{ \cancel{25} \: \: 5 \times {t}^{4} }{ \cancel{40} \: 8} }$

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$\large \boxed{ \: \: \mathtt{= \: \: \frac{5}{8} {t}^{4} \: \: }}$

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