Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is expressed as a fraction, where the numerator indicates the power and the denominator indicates the root.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent a^(m/n) to radical form, it can be expressed as the n-th root of a raised to the m power: a^(m/n) = n√(a^m).

Front

What is the value of 2^(1/6)?

Back

2^(1/6) represents the sixth root of 2.

Front

What does a negative exponent indicate?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent: a^(-n) = 1/(a^n).

Front

How do you simplify (5x)^(-5/4)?

Back

(5x)^(-5/4) can be simplified to 1/((5x)^(5/4)).

Front

What is the value of m^(-0.5)?

Back

m^(-0.5) is equivalent to 1/(√m) or 1/(m^(1/2)).

Front

How do you evaluate 6^(3/2)?

Back

6^(3/2) can be evaluated as √(6^3) or (√6)^3.

Front

What does 7^(4/3) represent?

Back

7^(4/3) represents the cube root of 7 raised to the fourth power: 7^(4/3) = ³√(7^4).

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents provide a way to express roots in exponential form, where the denominator of the exponent indicates the root.

Front

How can you multiply two expressions with rational exponents?

Back

To multiply two expressions with rational exponents, you can add the exponents if the bases are the same: a^(m/n) * a^(p/q) = a^((mq + np)/(nq)).