Why is a number to the first power equal that number?

Answer 1

For positive integer exponents, the exponent tells you how many times to take the base (the number being raised) as a factor then multiply.

So x^3 = x * x * x (3 times). x^2 = x * x (2 times). x^1 = x (1 time).

For negative exponents, do the same thing, but then take the reciprocal (1 divided by the number) to get the answer.

Exponent of zero is defined to equal 1, for any nonzero base number.

Rational exponents equate to taking a root (square root for 1/2, cube root for 1/3, etc).

Irrational exponents cannot use these methods, but require using logarithms to solve.