Exponents And Radicals — Chapter Summary

The notation for writing the product

The notation for writing the product of a number by itself several times is called exponential notation or exponential form. In a number such as 7^2,

The main laws

The main laws are: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m-n) when m > n, a^m ÷ a^n = 1/a^(n-m) when n > m, (a^m)^n = a^(mn), a^0 = 1 for any non-zero r

The expression a^(1/q) is defined as

The expression a^(1/q) is defined as the qth root of a. More generally, a^(p/q) = qth root of a^p, where a is positive. This connects powers and roots

Any natural number other than 1

Any natural number other than 1 can be expressed uniquely, apart from order, as a product of powers of prime numbers.

A surd is a positive irrational

A surd is a positive irrational number of the form nth root of x, where x is a positive rational number and the nth root cannot be found exactly. When