Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is expressed as a fraction, where the numerator indicates the power and the denominator indicates the root.

Front

How do you express the square root of x in terms of rational exponents?

Back

The square root of x can be expressed as x^(1/2).

Front

What is the first step in simplifying a value with a rational exponent?

Back

The first step is to take the root, as indicated by the denominator of the rational exponent.

Front

If you have x^(3/4), what does the 3 represent?

Back

The 3 represents the power to which the base x is raised after taking the fourth root.

Front

How do you convert x^(1/n) into radical form?

Back

x^(1/n) can be expressed as the nth root of x, written as √[n]{x}.

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents provide a way to express roots and powers in a single notation, where a rational exponent can be converted to a radical.

Front

Simplify: (x^(1/3))^2

Back

The simplified form is x^(2/3).

Front

What is the value of 8^(2/3)?

Back

The value is 4, since 8^(1/3) = 2 and then 2^2 = 4.

Front

If a^(m/n) = b, what is the equivalent radical form?

Back

The equivalent radical form is b = √[n]{a^m}.

Front

What happens when you multiply two expressions with the same base and rational exponents?

Back

You add the exponents: a^(m/n) * a^(p/q) = a^((mq + np)/(nq)).