Question

Solve: 27*3⁻²ᵛ⁺²=1/243

Answer 1

The solution to the equation
`\(27 * 3^(-2v+2) = (1)/(243)\)` is "
`\(v = -1\)`".

Step-by-step explanation:

To solve the given equation, we can start by simplifying the expression on the left side. Since
`\(3^(-2v+2)\)` is equivalent to
`\((1)/(3^(2v-2))\)`, the equation becomes
`\(27 * (1)/(3^(2v-2)) = (1)/(243)\)`.

Next, we can express 27 as
`\(3^3\)` and rewrite the equation as
`\((3^3)/(3^(2v-2)) = (1)/(243)\)`. Using the rule for dividing exponents with the same base, we subtract the exponents, resulting in
`\(3^(3-(2v-2)) = (1)/(243)\)`.

Simplifying further, we get
`\(3^(5-2v) = (1)/(243)\)`. Now, we can equate the exponents, leading to
`\(5-2v = -5\)`. Solving for
`\(v\)`, we find
`\(v = -1\)`.

Therefore, the solution to the equation
`\(27 * 3^(-2v+2) = (1)/(243)\)` is "
`\(v = -1\)`".