Solving 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

Simplify: 8^(1/3)

Back

2

Front

Evaluate: 64^(3/2)

Back

512

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents can be expressed as roots. For example, x^(m/n) = n√(x^m).

Front

Simplify: (x^(1/2))^4

Back

x^2

Front

What does the expression x^(-n) represent?

Back

x^(-n) represents the reciprocal of x raised to the positive n, or 1/(x^n).

Front

Evaluate: 100^(-1/2)

Back

1/10

Front

What transformation occurs when a function is reflected across the x-axis?

Back

The y-values of the function are multiplied by -1.

Front

If a cubic function is shifted right 5 units, what is the new function form?

Back

f(x) = (x - 5)^3.

Front

What is the effect of a negative exponent on a base?

Back

A negative exponent indicates that the base should be taken as a reciprocal. For example, a^(-n) = 1/(a^n).