Elementary Algebra: Applying the Exponent Rule for Negative Exponents

Flashcards covering negative exponent rules and algebraic simplification problems from Activity 9.

Negative Exponent Rule

The algebraic rule stating that $a^{-n} = \frac{1}{a^n}$ for $a \neq 0$.

Simplified form of $x^{-2}$

$$\frac{1}{x^2}$$

Simplified form of $y^{-1}$

$$\frac{1}{y}$$

Simplified form of $(2x)^{-1}$

$$\frac{1}{2x}$$

Simplified form of $2x^{-2}$

$$\frac{2}{x^2}$$

Simplified form of $4x^{-3}$

$$\frac{4}{x^3}$$

Simplified form of $(2x)^{-2}$

$$\frac{1}{4x^2}$$

Simplified form of $\frac{1}{x^{-12}}$

$$x^{12}$$

Simplified form of $\frac{4}{x^{-3}}$

$$4x^3$$

Simplified form of $\frac{2x}{y^{-3}}$

$$2xy^3$$

Simplified form of $\frac{x^2y^{-3}}{z^{-1}}$

$$\frac{x^2z}{y^3}$$

Simplified form of $\frac{12x^{-3}}{3x^{-2}}$

$$\frac{4}{x}$$

Simplified form of $\frac{x^2y^2}{(2xy)^{-3}}$

$$8x^5y^5$$

Simplified form of $\left(\frac{x}{y}\right)^{-2}$

$$\frac{y^2}{x^2}$$

Simplified form of $\left(\frac{3x}{4}\right)^{-2}$

$$\frac{16}{9x^2}$$

Simplified form of $\left(\frac{3x}{2yz}\right)^{-3}$

$$\frac{8y^3z^3}{27x^3}$$