If 5^m × 5³ × 5⁻²/5⁻⁵ = 5¹². Find m

Solution:

Given, 5^m × 5³ × 5⁻²/5⁻⁵ = 5¹².

We have to find the value of m.

Using law of exponents,

a^m × aⁿ = a^{m + n}

5^m × 5^{3 - 2}/5⁻⁵ = 5¹²

5^m × 5/5⁻⁵ = 5¹²

Using law of exponents,

a^m ÷ aⁿ = a^{m - n}

5^m × 5^{1 + 5} = 5¹²

5^m × 5⁶ = 5¹²

Now, 5^{m + 6} = 5¹²

m + 6 = 12

m = 12 - 6

m = 6

Therefore, the value of m is 6.

✦ Try This: If 6^m × 6⁴ × 6⁻²/6⁻⁵ = 6². Find m.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 122

If 5^m × 5³ × 5⁻²/5⁻⁵ = 5¹². Find m

Summary:

If 5^m × 5³ × 5⁻²/5⁻⁵ = 5¹². The value of m is 6 using the laws of exponents

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