rational exponents

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^(1/2) is the square root of x.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent to radical form, use the formula: a^(m/n) = n√(a^m), where m is the numerator and n is the denominator.

Front

Simplify: 16^(1/4)

Back

2

Front

Simplify: 27^(2/3)

Back

9

Front

What is the relationship between rational exponents and roots?

Back

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

Front

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

Back

√(x^3) or (√x)^3.

Front

Simplify: (x^(1/2))^4

Back

x^2

Front

What is the value of 64^(3/6)?

Back

16

Front

If a^(m/n) = b, what is the equivalent expression in radical form?

Back

b = n√(a^m).

Front

Simplify: (x^(1/3) * x^(2/3))

Back

x^(1) or x.