Powers Unit Review

This set of vocabulary flashcards covers the fundamental concepts of powers and exponents, including the six exponent laws, standard form, and mathematical modeling for population growth based on the unit review.

Power

A mathematical expression consisting of a base and an exponent, such as $3^{5}$.

Base

The number in a power that is being multiplied repeatedly; for example, in $(-3)^{2}$, the base is $-3$.

Exponent

The number that indicates how many times the base is used as a factor in repeated multiplication; for example, in $4^{3}$, the exponent is $3$.

Repeated Multiplication

The process of writing out a power as a sequence of factors; for example, $3^{4}$ is written as $3 \times 3 \times 3 \times 3$.

Standard Form

The numerical value resulting from evaluating a power; for example, the standard form of $2^{3}$ is $8$.

Product Law of Powers

The rule stating that when multiplying powers with the same base, you add the exponents, such as $4^{6} \times 4^{2} = 4^{8}$.

Quotient Law of Powers

The rule stating that when dividing powers with the same base, you subtract the exponents, such as $3^{7} \tan(3^{5}) = 3^{2}$.

Power of a Power Law

The rule stating that to raise a power to an exponent, you multiply the exponents, represented as $(a^{m})^{n} = a^{m \times n}$.

Zero Exponent Law

The rule stating that any non-zero base raised to the power of zero is equal to one ($a^{0} = 1$), as seen in $15^{0} = 1$.

Power of a Product Law

The rule stating that an exponent outside parentheses applies to every factor inside the parentheses, such as $(ab)^{n} = a^{n}b^{n}$.

Power of a Quotient Law

The rule stating that an exponent applies to both the numerator and the denominator in a division, such as $(\frac{a}{b})^{n} = \frac{a^{n}}{b^{n}}$.

Sadiq's Bacteria Growth Expression

The expression $2^{x}$ used to solve for a population that starts with one cell and doubles every hour, where $x$ represents the number of hours.

Ayesha's Bacteria Growth Variables

A growth scenario where a population starts with $2$ cells and quadruples ($\times 4$) every $15$ minutes over a period of $4$ hours.

Rabbit Population Projection

The calculation for a park starting with $12$ rabbits where the population grows by six times each year for $4$ years ($12 \times 6^{4}$).