Rational Exponents and Radicals Review

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(m/n) means the nth root of x raised to the m power.

Front

Convert 4^(5/2) to a radical expression.

Back

√(4^5) = √(1024) = 32.

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents can be expressed as radicals. For example, x^(1/n) is equivalent to the nth root of x.

Front

Write the expression ∛(x^7) in exponential form.

Back

x^(7/3).

Front

Simplify the expression 2^(3/2).

Back

√(2^3) = √8 = 2√2.

Front

What does the expression x^(m/n) represent?

Back

It represents the nth root of x raised to the m power.

Front

Convert y^(2/3) to a radical expression.

Back

∛(y^2).

Front

Simplify the expression 16^(1/4).

Back

2, since 16^(1/4) = √(√16) = √4 = 2.

Front

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

Back

8, since 8^(3/3) = 8^1 = 8.

Front

Write the expression √(x^5) in exponential form.

Back

x^(5/2).