(2/9)^3×(2/9)^(-6)=(2/9)^(2m-1)
Hmmm. I thought Reiny already showed how to do this one.
(2/9)^3×(2/9)^(-6)=(2/9)^(2m-1)
(2/9)^(3-6) = (2/9)^(2m-1)
-3 = 2m-1
m = -1
It's better to use * for multiplication online, since the variable x is easy to confuse with ×
if the bases are the same , you can add the exponents
(2/9)^3 × (2/9)^(-6) = (2/9)^(3-6) = (2/9)^(-3)
(2/9)^(-3) = (2/9)^(2m - 1)
To solve this equation, we can start by simplifying the left side of the equation by multiplying the two fractions together.
(2/9)^3 * (2/9)^(-6)
To multiply two numbers with the same base raised to different exponents, we can add the exponents together. In this case, the base is (2/9), so we can add the exponents:
(2/9)^(3 + -6)
Simplifying the exponents:
(2/9)^(-3)
Now, we can rewrite the right side of the equation as (2/9)^(2m-1).
(2/9)^(2m-1)
Since the bases are the same, we can set the exponents equal to each other:
-3 = 2m - 1
Now, we can solve for m.
-3 + 1 = 2m
-2 = 2m
To isolate m, we divide both sides of the equation by 2.
-2/2 = 2m/2
-1 = m
Therefore, the value of m that satisfies the equation (2/9)^3 * (2/9)^(-6) = (2/9)^(2m-1) is m = -1.