In this we are going to talk about Exponents laws and their use in Radicals-

Product law– if two factors raised to an exponent are being multiplied together, and they have the same base, we can add the exponents

 

Quotient law- If two factors raised to an exponent are being divided together, and they have the same base, we can subtract the exponents

 

Power of a Product law-

we can simplify a power of a power by multiplying the exponents and keeping the same base.

 

Power of a Quotient law-

The power of a quotient is equal to the power of each term in the numerator and denominator individually.

Power of a Power law-

if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same.

Integral Exponents-

If there is a negative power we flip the power and make it the exponent is in the denominator which makes it positive.

 

These are all the laws that we can use in radicals-

 

 

 

Rational Exponents-

if there is a fractional power, the number in the denominator is the root and the numerator is the number multiplying.

 

This law is the main one that we learned

Now we can write any power as Radicals and vice versa.

 

Power as Radicals-

 

Radicals as Power-