Converting between Radicals and Rational Exponents

Front

What is the relationship between radicals and rational exponents?

Back

Radicals can be expressed as rational exponents. For example, √a = a^(1/2).

Front

Convert the radical expression √x to exponential form.

Back

x^(1/2)

Front

What is the radical form of x^(3/4)?

Back

√(x^3) = 4√(x^3) (4th root of x cubed).

Front

Rewrite the expression x^(1/3) in radical form.

Back

√[3]{x} (the cube root of x).

Front

What is the exponential form of the expression √(y^5)?

Back

y^(5/2) (y raised to the power of 5/2).

Front

Convert the expression 4√(z^2) to exponential form.

Back

z^(2/4) = z^(1/2).

Front

What is the radical form of x^(5/2)?

Back

√(x^5) = 2√(x^5) (2nd root of x to the 5th).

Front

Rewrite the expression 1/√(a) in exponential form.

Back

a^(-1/2).

Front

What is the relationship between the index of a radical and the denominator of a rational exponent?

Back

The index of the radical corresponds to the denominator of the rational exponent. For example, the cube root corresponds to 1/3.

Front

Convert the expression 2√(b^6) to exponential form.

Back

b^(6/2) = b^3.