rational exponents

Front

What are rational exponents?

Back

Rational exponents are exponents that can be expressed as a fraction, where the numerator is an integer and the denominator is a positive integer. For example, x^(1/2) is a rational exponent.

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

What is the simplified form of (x^(1/2))^2?

Back

The simplified form is x.

Front

What is the value of 8^(1/3)?

Back

The value of 8^(1/3) is 2.

Front

How do you simplify (a^(m/n))^p?

Back

To simplify (a^(m/n))^p, multiply the exponents: a^(m/n * p).

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; for example, x^(1/n) represents the n-th root of x.

Front

Simplify the expression (64x^7)^(1/3).

Back

The simplified expression is 4x^2√[3]{x}.

Front

What is the simplified form of (144x^6y^(2/3))^(1/2)?

Back

The simplified form is 12x^3y^(1/3).

Front

If a^(m/n) = b, what is the value of a?

Back

To find a, raise both sides to the power of n: a = b^(n/m).

Front

What is the value of 27^(2/3)?

Back

The value of 27^(2/3) is 9.