Question

Find the value of 'm' : (3/8) 2m × (3/8)^6 × (3/8) = (3/8)^13​

Answer 1

The value is m = 3.

Explanation:

Multiplication of terms with same base and different exponents:

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents.

In this question:

We have the following expression:

`((3)/(8))^(2m) * ((3)/(8))^6 * ((3)/(8)) = ((3)/(8))^13`

Applying the property:

`((3)/(8))^(2m+6+1) = ((3)/(8))^13`

`((3)/(8))^(2m+7) = ((3)/(8))^13`

Since the bases are equal, we can equalize the exponents:

`2m + 7 = 13`

`2m = 6`

`m = (6)/(2) = 3`

The value is m = 3.