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Question 1 of 5: Simplify:
$$\sqrt{81},-\sqrt{15^2},\sqrt[3]{216}$$ $$\sqrt{81}$$$$-\sqrt{15^2}$$$$\sqrt[3]{216}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$\sqrt{81}=3,-\sqrt{15^2}=225,\sqrt[3]{216}=12$$ $$\sqrt{81}=3$$$$-\sqrt{15^2}=225$$$$\sqrt[3]{216}=12$$
B
$$\sqrt{81}=9,-\sqrt{15^2}=-15,\sqrt[3]{216}=6$$ $$\sqrt{81}=9$$$$-\sqrt{15^2}=-15$$$$\sqrt[3]{216}=6$$
C
$$\sqrt{81}=9,-\sqrt{15^2}=5,\sqrt[3]{216}=4$$ $$\sqrt{81}=9$$$$-\sqrt{15^2}=5$$$$\sqrt[3]{216}=4$$
D
$$\sqrt{81}=6,-\sqrt{15^2}=-3,\sqrt[3]{216}=14$$ $$\sqrt{81}=6$$$$-\sqrt{15^2}=-3$$$$\sqrt[3]{216}=14$$
E
$$\sqrt{81}=3,-\sqrt{15^2}=-15,\sqrt[3]{216}=4$$ $$\sqrt{81}=3$$$$-\sqrt{15^2}=-15$$$$\sqrt[3]{216}=4$$
Question 2 of 5: Simplify:
$$(-2187)^\frac{1}{7},(1296)^\frac{1}{4},-(512)^\frac{1}{9}$$ $$(-2187)^\frac{1}{7}$$$$(1296)^\frac{1}{4}$$$$-(512)^\frac{1}{9}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$(-2187)^\frac{1}{7}=-9,(1296)^\frac{1}{4}=12,-(512)^\frac{1}{9}=-8$$ $$(-2187)^\frac{1}{7}=-9$$$$(1296)^\frac{1}{4}=12$$$$-(512)^\frac{1}{9}=-8$$
B
$$(-2187)^\frac{1}{7}=3,(1296)^\frac{1}{4}=9,-(512)^\frac{1}{9}=4$$ $$(-2187)^\frac{1}{7}=3$$$$(1296)^\frac{1}{4}=9$$$$-(512)^\frac{1}{9}=4$$
C
$$(-2187)^\frac{1}{7}=-3,(1296)^\frac{1}{4}=6,-(512)^\frac{1}{9}=-2$$ $$(-2187)^\frac{1}{7}=-3$$$$(1296)^\frac{1}{4}=6$$$$-(512)^\frac{1}{9}=-2$$
D
$$(-2187)^\frac{1}{7}=6,(1296)^\frac{1}{4}=8,-(512)^\frac{1}{9}=-6$$ $$(-2187)^\frac{1}{7}=6$$$$(1296)^\frac{1}{4}=8$$$$-(512)^\frac{1}{9}=-6$$
E
$$(-2187)^\frac{1}{7}=-6,(1296)^\frac{1}{4}=16,-(512)^\frac{1}{9}=-18$$ $$(-2187)^\frac{1}{7}=-6$$$$(1296)^\frac{1}{4}=16$$$$-(512)^\frac{1}{9}=-18$$
Question 3 of 5: Simplify, assume all variables represent positive real numbers:
$$\frac{(27x^2)^\frac{1}{3}x^\frac{1}{3}}{x^\frac{2}{3}}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$9x$$
B
$$3x^\frac{1}{3}$$
C
$$81x^{-\frac{4}{3}}$$
D
$$1$$
E
$$729x^{\frac{2}{3}}$$
Question 4 of 5: Simplify, assume all variables represent positive real numbers:
$$\frac{(xz)^\frac{1}{9}x^\frac{2}{3}z^\frac{1}{3}}{(xz)^\frac{4}{9}}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$x^\frac{2}{9}z^\frac{5}{3}$$
B
$$xz^\frac{1}{3}$$
C
$$x^\frac{7}{3}z^\frac{2}{3}$$
D
$$x^\frac{1}{3}$$
E
$$z^\frac{1}{3}$$
Question 5 of 5: Simplify, assume all variables represent positive real numbers:
$$\left(\frac{2^{-2}z^{-\frac{3}{4}}x^{-\frac{1}{2}}}{z^\frac{5}{4}x^{-\frac{1}{3}}}\right)^{-3}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$8xz^\frac{2}{3}$$
B
$$128x^\frac{3}{2}z^{18}$$
C
$$4x^\frac{9}{10}z^\frac{1}{3}$$
D
$$16x^\frac{2}{3}z^\frac{3}{2}$$
E
$$64x^\frac{1}{2}z^6$$

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