6.9 Rational exponents
Exponents are always used in mathematical expressions. Exponents tells us how many times a number is multiplied to itself, like if we were ask to solved $5^7$, this would be just mean to multiply 5 to itself seven times. In the given expression $5^7$m 5 is the base, and 7 is the exponent. Through the help of exponents calculator you could easily compute the solution by just plugging in the given numbers. Buy If you were given $(5^3+ 2b)^7$ to evaluate, or an expression that would involve more exponents, it would be best to acquaint yourself with the exponent rules. These rules would guide us in simplifying expressions that contains exponents.
There a lot of different rules like the product rule where the exponents are added to each other provided that the bases are the same. Then, there is the quotient rule which states that if the bases are divided with each other you can just subtract the exponents, provided again that the bases are the same. There is also the power rule, where a base and an exponent are raised to another exponent where you would only need to multiply the exponents. Lastly, we would also look at the negative exponent rule which suggests that any base raised to a negative exponent will basically mean that you need to divide the base by the number denoted by the exponent. Each of the sections of this chapter will discuss each rule in depth and session 7 will be teaching us to integrate these rules and combine them all together. There’s also going to be a formula sheet for the exponent rules for you to easily understand and remember them.
This chapter would also discuss scientific notation, a technique used to express very large or very small numbers through the use of the base 10, raised to an exponent. We would also be converting rational exponents into radical exponents and vice versa and solving problems that involve exponents.
Rational exponents
Lessons
Notes:
${A^{x/y}} = {^y}\sqrt{A^x}$

1.
Write the following in the radical form

2.
Write the answer with positive exponents and then as entire radical

3.
Write the answer as a power and evaluate