Question

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

Answer 1

Answer:

The value is m = 3.

Step-by-step 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:

$(\frac{3}{8})^{2m} \times (\frac{3}{8})^6 \times (\frac{3}{8}) = (\frac{3}{8})^13$

Applying the property:

$(\frac{3}{8})^{2m+6+1} = (\frac{3}{8})^13$

$(\frac{3}{8})^{2m+7} = (\frac{3}{8})^13$

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

$2m + 7 = 13$

$2m = 6$

$m = \frac{6}{2} = 3$

The value is m = 3.