Powers, Exponents, and Negative Powers

Vocabulary and rule-based flashcards reviewing exponents, bases, repeated multiplication, and the rules governing negative bases and negative signs with powers.

Base

The number in an exponential expression that is being multiplied repeatedly (e.g., in $4^3$, the base is $4$).

Exponent

The power that indicates how many times the base is used in repeated multiplication (e.g., in $4^3$, the exponent is $3$).

Repeated multiplication

The expanded form of a power showing the base multiplied by itself the number of times indicated by the exponent (e.g., $4^3 = 4 \times 4 \times 4$).

Zero exponent

A power with an exponent of $0$, which always evaluates to $1$ (e.g., $6^0 = 1$).

Negative sign outside brackets rule

A rule stating that a negative sign on the outside of brackets means to multiply the evaluated answer by $(-1)$.

Negative base rule

A rule stating that a base is only negative when it is enclosed in brackets.

Negative sign without brackets rule

A rule stating that if an expression lacks brackets but has a negative sign, it is treated as having brackets around the base and power with the negative sign on the outside.

Evaluation of $(-3)^2$

An expression with a base of $-3$ that expands to repeated multiplication of $(-3) \times (-3)$ and evaluates to the standard form of $9$.

Evaluation of $-(3)^2$

An expression with a base of $3$ that expands to $-(3 \times 3)$ and evaluates to the standard form of $-9$.

Evaluation of $-3^2$

An expression with a base of $3$ that expands to $-1 \times (3 \times 3)$ and evaluates to the standard form of $-9$.

Evaluation of $-(2)^5$

An expression with a base of $2$ that expands to $-(2 \times 2 \times 2 \times 2 \times 2)$ and evaluates to the standard form of $-32$.

Evaluation of $(-4)^3$

An expression with a base of $-4$ that expands to $(-4) \times (-4) \times (-4)$ and evaluates to the standard form of $-64$.

Evaluation of $-7^6$

An expression with a base of $7$ that expands to $-(7 \times 7 \times 7 \times 7 \times 7 \times 7)$ and evaluates to the standard form of $-117,649$.