Algebra Flashcards
If you have a quantity raised to a power and that expression raised to another power, what do you do with the exponents?
You multiply them.
When adding fractions with variables (or algebraic expressions) in one or more denominators, what will the LCD look like?
The LCD will have each variable (or algebraic expression) to its highest power as a factor.
How do you express the reciprocal of a^n?
This property says that “a^(-1)” is the reciprocal of “a”. In other words, “a^(-1)” means ‘‘invert a.’’
So the answer would be a^(-n) which is 1/a^n.
If a positive exponent n means repeated multiplication of its base n times, what does a negative exponent -n mean for its base?
It means repeated multiplication of its reciprocal.
How can you express as separate terms two different bases that are being multiplied and their product is being raised to a power?
As each of the bases being raised to that power individually and then being multiplied together.
(ab)^n=(a^n)*(b^n)
Applying the properties of exponents, how can you express two different bases that are being divided and their division is being raised to a power?
As each of the bases being raised to that power individually and then being one being the numerator and the other the denominator of a fraction.
How do you convert a fraction into a product?
You multiply the denominator’s exponent by negative one.
Applying the properties of roots, how can you express the nth root of the product of “a” and “b” as individual roots?
As the nth root of “a” multiplied by the nth root of “b”.
ab)^(1/n) = (a)^(1/n) * (b)^(1/n
Applying the properties of roots, how can you express the nth root of the quotient of “a” by “b” as individual roots?
As the nth root of “a” divided by the nth root of “b”.
ab)^(1/n) = (a)^(1/n) / (b)^(1/n
Applying the properties of roots, how can you express the nth root of “a”, all raised to the power of “m”?
As the nth root of “a^m” or as “a^(m/n)”.
What is the nth root of “a”, all raised to the power of “n”?
“a”
What is the problem with having a root in the denominator of an expression? What can be done about it?
The expression is not simplified. To eliminate the root in the denominator you need to write the denominator as the nth root of some quantity to the nth power. That is accomplished by multiplying both the numerator and the denominator by an expression that eliminates the root in the denominator.
