Math, asked by omhasarmani783, 9 days ago

find Value of this
(\frac{3}{5})^{-2}

Answers

Answered by hukam0685
0

Step-by-step explanation:

Given: \left(\frac{3}{5}\right)^{-2}\\

To find: Find the value of above expression.

Solution:

Tip:

1) \bf \left( { \frac{a}{b} }\right)^{n}  =  \frac{ {a}^{n} }{ {b}^{n} }  \\

2) \bf {a}^{ - n}  =  \frac{1}{ {a}^{n} }\\

Step 1: Separate the power.

Use formula number 1.

\left(\frac{3}{5}\right)^{-2}=  \frac{ {3}^{ - 2} }{ {5}^{ - 2} }  \\

Step 2: Convert into positive powers.

Use formula number 2.

 \frac{ {3}^{ - 2} }{ {5}^{ - 2} }  =  \frac{ \frac{1}{ {3}^{2} } }{  \frac{1}{ {5}^{2} } }  \\

Step 3: Simplify and solve.

\frac{ \frac{1}{ {3}^{2} } }{  \frac{1}{ {5}^{2} } }  =  \frac{1}{ {3}^{2} }  \times  \frac{ {5}^{2} }{1}  \\

or

 =  \frac{ {5}^{2} }{ {3}^{2} }  \\

or

 =  \frac{25}{9}  \\

Final answer:

\bf \left(\frac{3}{5}\right)^{-2}=\frac{25}{9}\\

Hope it helps you.

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