The value of 'm' for which 5^m \div 5^{-3} \times 5^{10} = 5^{15} is:

Madhya Pradesh Police Exam Model Paper 9

Question : 82 of 100

Marks: +1, -0

The value of 'm' for which

5^m ÷ 5^{-3} × 5^{10} = 5^{15}

is:

Solution:

Given

5^m ÷ 5^{-3} × 5^{10} = 5^{15}

Formula

a^x × a^y = a^{(x + y)}

a^x ÷ a^y = a^{(x - y)}

Calculation

5^m ÷ 5^{-3} × 5^{10 }= 5^{15}

= 5^{m - (-3)} + 10 = 5^{15}

= 5^{m + 13} = 5^{15}

Comparing Powers, we get

m + 13 = 15

∴ m is 2

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