Introduction:
In this problem, we are given the expression (-3)-3 and we need to find the number by which it should be multiplied so that the product is (-15)-1. To solve this problem, we can use the concept of multiplication and inverse operations.

Step 1: Express the given expressions as multiplication:
To make the problem easier to solve, we can rewrite the expressions as multiplications. The expression (-3)-3 can be written as (-1) * 3 * 1 * 3 and (-15)-1 can be written as (-1) * 15 * 1.

Step 2: Set up the equation:
Let's assume the number we need to find is 'x'. We can set up the equation as follows:

(-1) * 3 * 1 * 3 * x = (-1) * 15 * 1

Step 3: Simplify the equation:
We can simplify the equation by canceling out the common factors:

(-1) * 3 * 1 * x = (-1) * 15 * 1

-3x = -15

Step 4: Solve for 'x':
To solve for 'x', we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by -3:

(-3x)/(-3) = (-15)/(-3)

x = 5

Step 5: Verify the solution:
To verify our solution, we can substitute the value of 'x' back into the original equation and check if both sides are equal:

(-1) * 3 * 1 * 3 * 5 = (-1) * 15 * 1

-45 = -15

Since both sides of the equation are equal, our solution is correct.

Conclusion:
The number by which (-3)-3 should be multiplied so that the product is (-15)-1 is 5. We followed the steps of expressing the expressions as multiplication, setting up the equation, simplifying it, solving for 'x', and verifying the solution to arrive at the answer.

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