Power Properties and Negative Bases Lecture

Practice vocabulary and mathematical rules regarding negative bases, exponents, and the power property of fractions based on the lecture transcript.

Negative number raised to an odd power

A mathematical scenario where the result is always negative, such as $(-2)^3 = -8$.

Negative number raised to an even power

A mathematical scenario where the result is always positive, such as $(-2)^4 = 16$.

Calculator Parentheses

The symbols that must include the negative sign when evaluating exponents to ensure the negative counts and is not ignored.

Power Property of Fractions

A rule stating that when a fraction is raised to a power, the exponent goes to both the numerator and the denominator (e.g., $\left(\frac{5}{8}\right)^3 = \frac{5 \times 5 \times 5}{8 \times 8 \times 8}$).

Evaluating $\left(-\frac{4}{7}\right)^5$

The process of taking a negative fraction to the fifth power, which results in a negative answer because the exponent is odd.

$$2^5$$

The numerical value equal to $32$.

$$\left(\frac{x}{2}\right)^4$$

The exponential form of the expression $\frac{x}{2} \times \frac{x}{2} \times \frac{x}{2} \times \frac{x}{2}$.

Power to a Power Property

A step used in simplifying expressions after taking the numerator and denominator to a power and dividing coefficients.