What is exponentiation?
Q: What is exponentiation?
A: Exponentiation is an arithmetic operation on numbers that can be thought of as repeated multiplication.
Q: How is exponentiation written?
A: Exponentiation is usually written as x^y, where x is the base and y is the exponent. It can also be written using the ^ or ** signs, such as 2^4 or 2**4.
Q: What are some examples of exponentiation?
A: Examples of exponentiation include 5^3 = 5*5*5 = 125; x^2 = x*x; 1^x = 1 for every number x; and 4^(1/2) = sqrt(4) = 2.
Q: What does it mean when the exponent is equal to -1?
A: When the exponent is equal to -1, then the power is simply the reciprocal of the base (x^(-1) = 1/x).
Q: How do you calculate an irrational power of a base?
A: To raise a base a to an irrational xth power, we use an infinite sequence of rational numbers (xn), whose limit is x (a^x = lim n->infinity a^(x_n)).
Q: Are there any rules that make calculating exponents easier?
A: Yes, there are several rules which make calculating exponents easier. These include (a * b) ^ n = a ^ n * b ^ n; (a / b) ^ n = a ^ n / b ^ n; a ^ r * a ^ s=a ^ (r + s); and so on.
