nth Roots and Rational Exponents

Front

What is the definition of an nth root?

Back

The nth root of a number x is a number r such that r^n = x. It is denoted as \( \sqrt[n]{x} \) or x^(1/n).

Front

Convert the expression \( \sqrt[3]{8} \) to exponential form.

Back

The exponential form is \( 8^{1/3} \).

Front

Simplify the expression \( 16^{1/4} \).

Back

The simplified form is 2.

Front

What is the relationship between rational exponents and roots?

Back

A rational exponent \( a^{m/n} \) can be expressed as \( \sqrt[n]{a^m} \) or \( (\sqrt[n]{a})^m \).

Tags

CCSS.HSN.RN.A.2

Front

Rewrite the expression \( \sqrt{10} \) in rational exponent form.

Back

The rational exponent form is \( 10^{1/2} \).

Tags

CCSS.HSN.RN.A.2

Front

What is the value of \( (-32)^{1/5} \)?

Back

The value is \( -2 \).

Front

Convert the expression \( 27^{2/3} \) to radical form.

Back

The radical form is \( \sqrt[3]{27^2} \) or \( \sqrt[3]{729} \).

Tags

CCSS.HSN.RN.A.2

Front

What is the definition of a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a power and a root.

Tags

CCSS.HSN.RN.A.2

Front

Simplify the expression \( 32^{1/5} \).

Back

The simplified form is 2.

Front

Convert the expression \( 64^{3/6} \) to radical form.

Back

The radical form is \( \sqrt[2]{64^3} \) or \( \sqrt{64^3} \).

Tags

CCSS.HSN.RN.A.2