Rational Exponents and Radicals

Front

What is a rational exponent?

Back

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

Front

How do you convert a radical expression to exponential form?

Back

To convert a radical expression to exponential form, use the formula: \( \sqrt[n]{a^m} = a^{m/n} \), where \( n \) is the index of the root.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; for example, \( a^{1/n} \) is equivalent to \( \sqrt[n]{a} \).

Front

Simplify the expression \( 16^{3/4} \).

Back

The simplified form is 8.

Front

Evaluate \( 27^{2/3} \).

Back

The result is 9.

Front

What is the value of \( 64^{1/2} \)?

Back

The value is 8.

Front

How do you express \( \sqrt[3]{x^6} \) in exponential form?

Back

It can be expressed as \( x^{6/3} = x^2 \).

Front

What is the simplified form of \( 81^{3/4} \)?

Back

The simplified form is 27.

Front

Convert \( 8^{5/3} \) to radical form.

Back

It can be expressed as \( \sqrt[3]{8^5} \).

Front

What is the value of \( 100^{1/2} \)?

Back

The value is 10.