Properties of Rational Exponents Review

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a root and a power. For example, x^(1/2) is the square root of x.

Front

How do you convert a negative exponent to a positive exponent?

Back

To convert a negative exponent to a positive exponent, use the reciprocal of the base. For example, x^(-n) = 1/(x^n).

Front

What happens when you multiply like bases?

Back

When you multiply like bases, you add the exponents. For example, x^a * x^b = x^(a+b).

Front

What happens when you raise a power to another power?

Back

When you raise a power to another power, you multiply the exponents. For example, (x^a)^b = x^(a*b).

Front

What happens when you divide like bases?

Back

When you divide like bases, you subtract the exponents. For example, x^a / x^b = x^(a-b).

Front

What is the reciprocal of x^3?

Back

The reciprocal of x^3 is 1/(x^3) or x^(-3).

Front

What is the value of 2^(1/3) * 2^(2/3)?

Back

The value is 2^(1/3 + 2/3) = 2^1 = 2.

Front

What is the value of (x^(1/2))^4?

Back

The value is x^(1/2 * 4) = x^2.

Front

If x^5 / x^2 = x^n, what is n?

Back

n = 5 - 2 = 3.

Front

What is the value of 3^(-2)?

Back

The value is 1/(3^2) = 1/9.