Question

Simplify and give answer in positive index (5)^-4 × (4/5)^-4×2^8​

Answer 1

$\huge{\mathbb{\underline{\green{ANSWER}}}}$

${(5)}^{ - 4} \times {( \frac{4}{5} )}^{ - 4} \times {2}^{8} \\ = > \frac{1}{5 \times 5 \times 5 \times 5} \times \frac{5 \times 5 \times 5 \times 5}{4 \times 4 \times 4 \times 4} \times 256 \\ = > \frac{1}{256} \times 256 \\ = > 1$

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Answer 2

Solution :

$\sf \implies {(5)}^{ - 4} \times (\frac{4}{5})^{ - 4} \times {(2)}^{8} \\ \\\sf \implies {(5)}^{ - 4} \times \bigg (\frac{4}{5}\bigg)^{ - 4} \times { \bigg (({2)}^{ - 2}\bigg) }^{ - 4} \\ \\\sf \implies \bigg(5 \times \frac{4}{{5}} \times \frac{1}{4} \bigg)^{ - 4} \\\\ \sf \implies ({1)}^{ - 4} \\ \\\sf \implies \frac{1}{1^{4} } \\ \\ \Large \implies\sf1$

Identity used :

$\large \implies \boxed{ \sf{a}^{m} \times {b}^{m} = {ab}^{m}}$

Other important identities :

$\large\implies \sf {a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ \large\implies \sf{a}^{m} \div {a}^{n} = {a}^{m - n} \\ \\ \large\implies \sf {a}^{m} = {a}^{n} \: \: \: \: \: \: \: [ m = n]$