Algebraic Exponents and Radicals Simplification

Vocabulary practice flashcards matching each algebraic expression with its simplified equivalent expression.

$$3^{2-x}(27x^3)^{\frac{1}{3}}$$

$$3^{3-x}x$$

$$[(2x+3)(2x-3)]^2$$

$$16x^4 - 72x^2 + 81$$

$$x(x^{a-1})(x^{a-1})$$

$$x^{2a-1}$$

$$\frac{(x+y)^{-2}}{(x+y)^{-1}}$$

$$\frac{1}{x+y}$$

$$\frac{a^{n+1}}{a^{n-1}}$$

$$a^2$$

$$\left(\frac{7m^{-1}n^3}{n^2m^{-2}}\right)^{-2}$$

$$\frac{1}{49m^2n^2}$$

$$\left(\frac{1}{2}x^{-2}\right)^{-3}$$

$$8x^6$$

$$\frac{3^{x-1}+3^{x+1}}{3^{x+1}+3^{x+1}+3^{x+1}}$$

$$\frac{10}{27}$$

$$\left(\frac{1}{81}\right)^{-2x}\left(\left(\frac{1}{27}\right)^{-3}\right)^{-2}$$

$$3^{8x-18}$$

$$-\sqrt{(c-7d)^2}$$

$$-|c-7d|$$

$$\pm\sqrt{49(e-f)^2}$$

$$\pm 7|e-f|$$

$$\sqrt{(g+3)^2(g-3)^2}$$

$$|g^2-9|$$

$$\sqrt{4a^2-20a+25}$$

$$|2a-5|$$

$$\sqrt{1-6c+9c^2}$$

$$|1-3c|$$

$$\sqrt{\frac{m^2-2m-15}{4m-20}}$$

$$\frac{\sqrt{m+3}}{2}$$

$$\sqrt[4]{m^{12}(n-5)^8}$$

$$|m^3|(n-5)^2$$