Question

simplify (1/3)⁵ × 3⁵ × (2/3)²​

Answer 1

Answer:

Answer will be 4/9 or (2/3)²

Answer 2

Question:-

simplify (1/3)⁵ × 3⁵ × (2/3)²

Required formulae:-

$\frac{1}{ {a}^{m} } = {a}^{ - m}$

${a}^{m} \times {a}^{n} = {a}^{m + n}$

$( { \frac{a}{b} })^{m} = \frac{ {a}^{m} }{ {b}^{m} }$

${a}^{0} = 1$

Solution:-

$\frac{1}{ {3}^{5} } \: can \: be \: written \: as \: {3}^{ - 5}$

So, it becomes

${3}^{ - 5} \times {3}^{5} \times ( { \frac{2}{3} })^{2}$

By second formula

${3}^{ - 5 + 5} \times ( { \frac{2}{3} })^{2}$

By third formula,

${3}^{0} \times \frac{ {2}^{2} }{ {3}^{2} }$

By fourth formula

$1 \times \frac{4}{9}$

$= > \frac{4}{9}$

Final answer:-

$\frac{4}{9}$