(4²*5^-2)(4²/5²)

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Solution

Dear Purva,
You may take the following steps to approach this Q.

Steps:
Use the laws of exponents or else make the negative exponent as seen with 5, positive.
Let us simplify, using the laws of exponents:

$(\frac{4^{2}}{5^{- 2}}) \times (\frac{4^{2}}{5^{2}}) = (\frac{4^{2 + 2}}{5^{- 2 + 2}}) . . . . . . (a^{m} \times a^{n} = a^{m + n}) = \frac{4^{4}}{5^{0}} . . . . . (a^{0} = 1) = 4 \times 4 \times 4 \times 4 = 256$

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x = 5 - 5 sin t

y = 4 + 5 cos t

\frac{25}{k} = 1^{2} - \frac{2^{2}}{5} + \frac{3^{2}}{5^{2}} - \frac{4^{2}}{5^{3}} + \frac{5^{2}}{5^{4}} - \frac{6^{2}}{5^{2}} + . . . . . . \infty

k

1^{2} - \frac{2^{2}}{5} + \frac{3^{2}}{5^{2}} - \frac{4^{2}}{5^{3}} + \frac{5^{2}}{5^{4}} - \frac{6^{2}}{5^{5}} + . . . . .

1^{2} - \frac{2^{2}}{5} + \frac{3^{2}}{5^{2}} - \frac{4^{2}}{5^{3}} + \frac{5^{2}}{5^{4}} - \frac{6^{2}}{5^{5}} + . . . .

{(1 \frac{3}{5})}^{2} + {(2 \frac{2}{5})}^{2} + {(3 \frac{1}{5})}^{2} + 4^{2} + {(4 \frac{4}{5})}^{2} + . . . .,

\frac{16 m}{5}

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