Rational Exponents and Radical Form

Front

Write with rational exponents: √(7x)

Back

(7x)^(1/2)

Front

Rewrite the following: ∛x^5

Back

x^(5/3)

Front

What is the definition of 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

Convert the expression x^(1/2) to radical form.

Back

√x

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents represent roots; for example, x^(1/n) is equivalent to the nth root of x.

Front

Rewrite in radical form: x^(3/4)

Back

∛(x^3)√(x) (or 4th root of x^3)

Front

What is the value of (x^a)(x^b)?

Back

x^(a+b) (the product of powers property)

Front

What is the value of (x^a)/(x^b)?

Back

x^(a-b) (the quotient of powers property)

Front

Convert the expression 4^(3/2) to radical form.

Back

√(4^3) or 8

Front

What is the value of x^(0)?

Back

1 (any non-zero number raised to the power of zero is 1)