Powers and Negative Exponents

Vocabulary flashcards defining key rules and standard form evaluations for powers, negative bases, and bracket usage based on the lecture notes.

Negative Sign Outside of Brackets Rule

A negative sign $(-)$ on the outside of brackets means to multiply the final calculated answer by $(-1)$.

Negative Base Rule

A base is only treated as negative when it is enclosed within brackets.

Negative Sign Without Brackets Rule

If an expression has a negative sign without brackets, treat it as if brackets exist with the negative sign on the outside.

Evaluation of $(-3)^2$

The base is $-3$, the repeated multiplication is $(-3) \times (-3)$, and the standard form evaluates to $9$.

Evaluation of $-(3)^2$

The base is $3$, the repeated multiplication is $-(3 \times 3)$, and the standard form evaluates to $-9$.

Evaluation of $-3^2$

The base is $3$, the repeated multiplication is $-1 \times (3 \times 3)$, and the standard form evaluates to $-9$.

Evaluation of $-(2)^5$

The base is $2$, the repeated multiplication is $-(2 \times 2 \times 2 \times 2 \times 2)$, and the standard form evaluates to $-32$.

Evaluation of $-7^6$

The base is $7$, the repeated multiplication is $-1 \times (7 \times 7 \times 7 \times 7 \times 7 \times 7)$, and the standard form evaluates to $-117,649$.

Evaluation of $(-2)^4$

The base is $-2$, the exponent is $4$, the repeated multiplication is $(-2) \times (-2) \times (-2) \times (-2)$, and the evaluated answer is $16$.

Evaluation of $6^0$

The base is $6$, the exponent is $0$, and the evaluated answer is $1$.