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

Convert the expression x^(3/4) into radical form.

Back

x^(3/4) = 4√(x^3) or (4√x)^3.

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 (x^(1/2))^4.

Back

Using the power of a power property, (x^(1/2))^4 = x^(1/2 * 4) = x^2.

Front

What is the product of powers property?

Back

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

Front

Simplify the expression x^(2/3) * x^(1/3).

Back

Using the product of powers property, x^(2/3) * x^(1/3) = x^(2/3 + 1/3) = x^(3/3) = x.

Front

What is the quotient of powers property?

Back

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

Front

Simplify the expression x^(5/6) / x^(1/3).

Back

Using the quotient of powers property, x^(5/6) / x^(1/3) = x^(5/6 - 1/3) = x^(5/6 - 2/6) = x^(3/6) = x^(1/2).

Front

What is the zero exponent rule?

Back

The zero exponent rule states that any non-zero base raised to the power of zero equals one: a^0 = 1.

Front

Evaluate the expression 16^(3/4).

Back

16^(3/4) = (4√16)^3 = 4^3 = 64.