Powers of Monomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a number, a variable, or a product of numbers and variables raised to non-negative integer powers.

Front

What does it mean to raise a monomial to a power?

Back

Raising a monomial to a power means multiplying the monomial by itself a certain number of times, as indicated by the exponent.

Front

What is the result of (x^a)^b?

Back

The result is x^(a*b), according to the power of a power rule.

Front

What is the power of a power rule in exponents?

Back

The power of a power rule states that when raising a power to another power, you multiply the exponents.

Front

Calculate (x^2y^3)^2.

Back

The result is x^(2*2)y^(3*2) = x^4y^6.

Front

Calculate (r^4)^6.

Back

The result is r^(4*6) = r^24.

Front

Calculate (5^2)^3.

Back

The result is 5^(2*3) = 5^6.

Front

What happens when you multiply two monomials with the same base?

Back

You add the exponents of the like bases.

Front

What is the result of x^3 * x^2?

Back

The result is x^(3+2) = x^5.

Front

What is the result of (ab^2)^3?

Back

The result is a^3b^(2*3) = a^3b^6.