Explain in details the correct solution:
Simplify the expression.
(–3)^4
The answer is 81 but how would I explain the correct solution?
-3 * -3 = 9
9 * -3 = -27
-27 * -3 = 81
(-3)^4 = (-3)^2*(-3)^2 = 9 * 9 = 81.
Or (-3)^4 = -3 * -3 * -3 * -3 = 81.
To simplify the expression (-3)^4, we need to understand the concept of exponentiation. In mathematics, an exponent refers to the number of times a base number is multiplied by itself. In this case, the base number is -3 and the exponent is 4.
To find the solution, you can follow these steps:
1. Start by raising the base number, -3, to the power of 1: (-3)^1 = -3.
2. Multiply this result by the base number, -3, again: (-3)^1 * -3 = -9.
3. Continue this multiplication process until you reach the exponent, which is 4. Each time, you multiply the result by the base number (-3) once more.
Let me break it down step by step for clarity:
(-3)^1 = -3
(-3)^1 * -3 = -9
(-3)^2 = (-9) * (-3) = 27
(-3)^3 = (27) * (-3) = -81
(-3)^4 = (-81) * (-3) = 243
Based on these calculations, (-3)^4 equals 243, not 81 as mentioned in the question.
However, if the question states that the correct answer is 81, then there might be a mistake in the solution or the given expression. Please double-check the question and the provided answer to ensure accuracy.