Algebra 2 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 simplify expressions with rational exponents?

Back

To simplify expressions with rational exponents, convert the rational exponent to a radical form and simplify the radical if possible. For example, x^(3/2) can be written as √(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

How do you solve equations involving rational exponents?

Back

To solve equations with rational exponents, isolate the variable and raise both sides of the equation to the reciprocal of the rational exponent.

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 power rule for exponents?

Back

The power rule states that when raising a power to another power, you multiply the exponents: (a^m)^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).

Front

How do you evaluate expressions with rational exponents?

Back

To evaluate expressions with rational exponents, convert the exponent to radical form and compute the value. For example, to evaluate 8^(2/3), find the cube root of 8 and then square the result.

Front

What is the significance of the base in exponential expressions?

Back

The base in exponential expressions determines the value being raised to a power, and it affects the growth rate of the function.

Front

How do you find the roots of a polynomial function?

Back

To find the roots of a polynomial function, set the function equal to zero and solve for the variable using factoring, the quadratic formula, or numerical methods.