Question

plz fo it correct plz​

Answer 1

ANSWER :-

• Option (A) is correct. = 1/6

TO FIND :-

• The value of [(2)⁵ × (9)²]/[(8)² × (3)⁵]

SOLUTION :-

$\implies \bf \: \frac{(2) ^{5} \times (9) ^{2} }{(8) ^{2} \times (3) ^{5} } \\ \\ \implies \bf \: \frac{(2) ^{5} }{(8) ^{2} } \times \frac{(9) ^{2} }{(3) ^{5} } \\ \\ \implies \bf \frac{(2) ^{5} }{(2) ^{3 \times 2} } \times \frac{(3) ^{2 \times 2} }{(3) ^{2} }$

by using a^b ÷ a^c = a^b-c we get,

$\implies \bf \: (2) ^{5 - 6} \times (3)^{4 - 5} \\ \\ \implies \bf \: (2) ^{ - 1} \times (3) ^{ - 1}$

By using a^-n = 1/a^n we get,

$\implies \bf \frac{1}{2} \times \frac{1}{3} \\ \\ \implies \bf \frac{1}{6}$

Hence the value is 1/6.

ADDITIONAL INFORMATION :-

$\boxed{\begin{minipage}{6cm} \\ \bf{\underline{Laws of Exponents }} \\ \\ \sf{ a^m \times a^n = {a}^{m+n} }\\ \\ {a}^{m} \div {a}^{n} = {a}^{m-n} \\ \\\dfrac{ a^m }{b^m}= {\bigg(\dfrac{a}{b} \bigg)}^{m}\\ \\ {a}^{m} \times {b}^{m} = {(ab)}^{m} \\ \\ {a}^{0} = 1\end{minipage}}$

Answer 2

Answer:

Option A is the answer for your question.

Step by step solution is given in the attachment.

Step-by-step explanation:

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