Exponents and Radicals of Algebraic Expressions

Raising an algebraic expression to a power:

CASO 1.- monomials with positive base

10.41 Raise the expression:

Solution:

To raise an algebraic expression to a power, we raise each one of its factors to that power. When a number or letter variable doesn't have an exponent, it is understood the have 1 as an exponent. Since to raise a power to another we need to multiply those powers, we have:

10.42 Calculate:

Remember that if a base has a negative sign and it is has an even exponent, the result is positive.

Answer:

10.43 Calculate:

Solution:

First, we perform the operations found inside parenthesis. Remember that to

multiply powers with the same base, we need to add the exponents. To raise a power to another, multiply the exponents.

10.44 Calculate:

We raise the numerator and denominator to 3

To divide powers with the same base, we need to subtract the exponents:

Answer:

10.45 Calculate:

First, we perform the operations found inside parenthesis:

We multiply the powers with the same base in the numerator and denominator:

It is always a good idea to order your factors alphabetically. Divide the powers with the same base subtracting their exponents:

Raise the resulting fraction to the cube.

Answer: