Demonstrate the difference between the exponent and base of a power by representing two powers with exponent and base interchanged (e.g., $2^3$ and $3^2$ or $10^3$ and $3^10$) using repeated multiplication or concrete models and describe the result.

Predict which of two powers represents the greater quantity, explain the reasoning, and verify using technology.

Analyze the role of brackets in powers by using repeated multiplication [e.g., $(-2)^4$, $(-2^4)$, and $–2^4$] and generalize strategies for evaluating powers involving brackets.

Justify why $a^0, a ≠ 0$, must equal to 1.

Predict whether the value of a given power will be positive or negative (e.g., what will the sign of $-7^15$ be?).

Evaluate powers with integral bases (excluding base 0) and whole number exponents, with or without the use of technology.

Generalize, using repeated multiplication to represent powers, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents:

• $(a^m)(a^n)=a^{m+n}$
• $a^m/a^n =a^{m-n},m>n$
• $(a^m)^n = a^{mn}$
• $(ab)^m=a^mb^m$

Apply the exponent laws to expressions involving powers, and determine the quantity represented by the expression, with or without the use of technology.

Prove by contradiction that $a^m+a^n ≠ a^{mn}$, $a^m-a^n ≠ a^{m-n}$, and $a^m-a^n ≠ a^{m/n}$

Describe and apply strategies for evaluating sums or differences of powers.

Analyze a simplification of an expression involving powers for errors.