We have, ( 59)^2×( 35)^ 3 = ( 59)^2×( 53)^3 = 5^29^2×5^33^3 = 5^2 + 3( 3^2)^2×3^3 = 5^53^7 = 31252187 Hence, this is the answer. ...

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Byju's Answer

Standard XII

Mathematics

General Term of Binomial Expansion

Evaluate: 59...

Question

Evaluate:
${(\frac{5}{9})}^{2} \times {(\frac{3}{5})}^{- 3}$

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Solution

We have,
${(\frac{5}{9})}^{2} \times {(\frac{3}{5})}^{- 3} = {(\frac{5}{9})}^{2} \times {(\frac{5}{3})}^{3} = \frac{5^{2}}{9^{2}} \times \frac{5^{3}}{3^{3}} = \frac{5^{2 + 3}}{{(3^{2})}^{2} \times 3^{3}} = \frac{5^{5}}{3^{7}} = \frac{3125}{2187}$

Hence, this is the answer.

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Similar questions

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

Q. Evaluate:

\frac{7 + 3 \sqrt{5}}{7 - 3 \sqrt{5}} + \frac{7 - 3 \sqrt{5}}{7 + 3 \sqrt{5}} =

Q. Evaluate

\frac{\sqrt{5}}{\sqrt{3} + \sqrt{2}} - \frac{3 \sqrt{3}}{\sqrt{5} + \sqrt{2}} + \frac{2 \sqrt{2}}{\sqrt{5} + \sqrt{3}}

Q. Evaluate :

{(\frac{5}{9})}^{- 2} \times {(\frac{3}{5})}^{- 3} \times {(\frac{3}{5})}^{0}

Q. Evaluate:

{(\frac{5}{9})}^{- 2} \times {(\frac{3}{5})}^{- 3} \times {(\frac{3}{5})}^{0}

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Evaluate:(59)2×(35)−3

We have,(59)2×(35)−3=(59)2×(53)3=5292×5333=52+3(32)2×33=5537=31252187Hence, this is the answer.

Evaluate:
${(\frac{5}{9})}^{2} \times {(\frac{3}{5})}^{- 3}$

We have,
${(\frac{5}{9})}^{2} \times {(\frac{3}{5})}^{- 3} = {(\frac{5}{9})}^{2} \times {(\frac{5}{3})}^{3} = \frac{5^{2}}{9^{2}} \times \frac{5^{3}}{3^{3}} = \frac{5^{2 + 3}}{{(3^{2})}^{2} \times 3^{3}} = \frac{5^{5}}{3^{7}} = \frac{3125}{2187}$

Hence, this is the answer.