Q:

# What is a method for multiplying fractions with exponents?

A:

A good method for multiplying fractions with exponents is to factor, cancel and simplify. This works whether the exponent is attached to a variable or a numeral.

## Keep Learning

Credit: Glow Images N/A Getty Images

One example in which there are no variables is "(3^2 / 4^2) x (2^4 / 6^3)." In this case, the first step of factoring simply involves writing out all the exponents: "(3 x 3 / 4 x 4) x (2 x 2 x 2 x 2 / 6 x 6 x 6)," and then factoring again: "(3 x 3 / 2 x 2 x 2 x 2) x (2 x 2 x 2 x 2 / 2 x 3 x 2 x 3 x 2 x 3)." The second step requires canceling. All the numerators cancel out with two of the 3s and four of the 2s in the denominator, leaving only "1 / 2 x 2 x 2 x 3." The third step is to simplify, so in this case the denominator gets multiplied for the final answer: "1 / 24."

An example of a problem with variables is "[(x^2 + 3x + 2) / (2x^2 + 7x +3)] x [(2x^2 + 9x + 9) / (x^2 + 3x + 2)]." First, it needs to be factored: "[(x + 2) (x + 1) / (x + 3) (2x + 1)] x [(2x + 3) (x + 3) / (x + 2) (x + 1)]." Canceling comes next. Because there is an "(x + 2)," an "(x + 1)" and an "(x + 3)" in both the numerator and the denominator, all of them cancel each other out, leaving only "(2x + 3) / (2x + 1)." In this case, there is no simplifying to be done, so "(2x + 3) / (2x + 1)" is the final answer.

Sources:

## Related Questions

• A: The basic rule in adding and subtracting variables with exponents is they must be like terms. Like terms consist of the same variable or set of variables r... Full Answer >
Filed Under:
• A: The quotient of powers property states that when two powers with the same base are divided, the exponents are subtracted from each other. This is written o... Full Answer >
Filed Under:
• A: The steps for multiplying polynomials with exponents vary depending on the complexity of the polynomials. If the equation has only one variable, the answer... Full Answer >
Filed Under:
• A: Rational or fractional exponents are another way of notating that some root of a base number should be taken, without using a radical sign. For instance, 1... Full Answer >
Filed Under:
PEOPLE SEARCH FOR