Question

how do the exponents change from one row of the table to the next? to get to the next row of the table, decrease the exponent by ?. the table has two columns: $3^n$ and value. the rows are: $3^4$ with value 81, $3^3$ with value 27, $3^2$ with value 9, $3^1$ with value 3, $3^0$ with value ?.

Explanation:

Step1: Analyze exponent sequence

The exponents in the table are \(4\), \(3\), \(2\), \(1\), \(0\).

Step2: Calculate the difference

From \(4\) to \(3\): \(4 - 3 = 1\); from \(3\) to \(2\): \(3 - 2 = 1\); from \(2\) to \(1\): \(2 - 1 = 1\); from \(1\) to \(0\): \(1 - 0 = 1\). So the exponent decreases by \(1\) each time.

Answer:

\(1\)