Final answer:
To solve the equation 1/5ⁿ⁻⁹=5⁷ⁿ⁻⁴ using the like-bases property and exponents, set the exponents equal to each other and solve for n.
Step-by-step explanation:
To solve the equation 1/5ⁿ⁻⁹=5⁷ⁿ⁻⁴ using the like-bases property and exponents, we need to make sure the bases are the same on both sides of the equation. In this case, the bases are 1/5 and 5. We can write 1/5 as 5⁻¹, so the equation becomes:
5⁻¹ⁿ⁻⁹ = 5⁷ⁿ⁻⁴
Now, we can apply the like-bases property which states that if the bases are the same, the exponents must be equal. So we set the exponents equal to each other and solve for n:
-1n - 9 = 7n - 4
Combining like terms and solving for n, we find:
8n = -5
n = -5/8