The equation a' * a' = a' is a fundamental rule in mathematics known as the power rule. It states that when multiplying two numbers with the same base, the exponents are added together. In this case, a' is the same as a^1, so when multiplied by itself, the exponent is 1+1=2, resulting in a^2, which is equal to a.
In real life, this equation can be seen in various scenarios such as calculating the area of a square, where the length and width are both represented by a. In this case, a' * a' would be the same as a^2, giving us the total area of the square.
Yes, this equation can be extended to any power. For example, a^3 * a^4 = a^(3+4) = a^7. This follows the same rule of adding the exponents when multiplying numbers with the same base.
Yes, this equation is always true for any value of a. It is a fundamental rule in mathematics that has been proven to be true through various mathematical proofs.
When dealing with algebraic expressions, the power rule can be used to simplify them by combining like terms. For example, 2a * 3a = (2*3)a^(1+1) = 6a^2. This can help in solving equations and finding the value of variables.