Sure, let's solve the given equation step-by-step.
The equation provided is:
[tex]\[
\left(\frac{3}{8}\right)^{2m} \times \left(\frac{3}{8}\right)^{6} \times \left(\frac{3}{8}\right) = \left(\frac{3}{8}\right)^{13}
\][/tex]
To solve for [tex]\( m \)[/tex], we start by using the properties of exponents. If we have the same base for multiplication, we can add the exponents. Therefore:
[tex]\[
\left(\frac{3}{8}\right)^{2m + 6 + 1} = \left(\frac{3}{8}\right)^{13}
\][/tex]
Simplify the exponent on the left side:
[tex]\[
\left(\frac{3}{8}\right)^{2m + 7} = \left(\frac{3}{8}\right)^{13}
\][/tex]
Since the bases are the same, we can set the exponents equal to each other:
[tex]\[
2m + 7 = 13
\][/tex]
Next, solve this equation for [tex]\( m \)[/tex]:
[tex]\[
2m + 7 = 13
\][/tex]
Subtract 7 from both sides:
[tex]\[
2m = 6
\][/tex]
Divide both sides by 2:
[tex]\[
m = 3
\][/tex]
Therefore, the value of [tex]\( m \)[/tex] is:
[tex]\[
m = 3
\][/tex]
