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, a^(m/n) represents the n-th root of a raised to the m-th power.

Front

How do you convert a rational exponent to a radical expression?

Back

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

Front

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

Back

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

Front

Simplify the expression (x^(1/2))^2.

Back

The expression simplifies to x, because (x^(1/2))^2 = x^(1/2 * 2) = x^1 = x.

Front

What is the result of a^(1/2) * a^(1/2)?

Back

The result is a, because a^(1/2) * a^(1/2) = a^(1/2 + 1/2) = a^1 = a.

Front

How do you simplify (a^(1/2) b^(1/2))^(-1)?

Back

The expression simplifies to 1/(a^(1/2) b^(1/2)), which can also be written as 1/(√a * √b).

Front

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

Back

The simplified form of 27^(2/3) is 9, since 27^(1/3) = 3 and 3^2 = 9.

Front

If x^(3/4) = 16, what is x?

Back

To find x, raise both sides to the reciprocal of 3/4, which is 4/3: x = 16^(4/3) = 64.

Front

What is the product rule for exponents?

Back

The product rule states that when multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).