### Video Transcript

Write an equation in the form π¦ equals π to the power π₯ for the numbers in the table.

We are given three pairs of values. When π₯ equals one, π¦ equals negative three. When π₯ equals two, π¦ equals nine. And when π₯ equals four, π¦ is equal to 81. Letβs begin by considering π₯ equals one and π¦ equals negative three and substitute them into the equation π¦ equals π to the power of π₯.

As the exponent or power is equal to one, we have negative three is equal to π to the power of one. As any value to the power of one is itself, π is equal to negative three. As this is the only unknown we needed to calculate, we can rewrite the equation as π¦ equals negative three to the power of π₯.

At this stage, it is worth checking whether this equation works for our other two pairs of values. Substituting π₯ equals two and π¦ equals nine gives us nine is equal to negative three squared. Multiplying a negative number by a negative gives a positive answer. Therefore, negative three squared is nine. The equation works for the second set of values.

Substituting π₯ equals four and π¦ equals 81 gives us 81 is equal to negative three to the power of four. Raising negative three to the fourth power is the same as negative three multiplied by negative three multiplied by negative three multiplied by negative three. This is the same as nine multiplied by nine. Negative three to the fourth power is 81. Therefore, the third set of values also works for this equation.

For the numbers in the table, the correct equation is π¦ is equal to negative three to the power of π₯.