For Problems 1-14 Simplify:
1) \(\sqrt[3]{54}\)
2) \(\sqrt[5]{96b^{15}}\)
3) \(\sqrt[4]{162x^{11}y^6}\)
4) \(\sqrt[4]{27x^3}\cdot \sqrt[4]{9x^2}\)
5) \(-11\sqrt[4]{12}\cdot 3\sqrt[4]{20}\)
6) \(\sqrt[3]{2a^{10}}\cdot \sqrt[3]{24a^4}\)
7) \(5\sqrt[3]{36x^{5}}\cdot 2\sqrt[3]{12x^{14}}\)
8) \(4\sqrt[6]{x}+13\sqrt[6]{x}\)
9) \(3\sqrt[4]{32}+\sqrt[4]{1250}\)
10) \(7x\cdot\sqrt[3]{54y^7}-5xy^2\cdot\sqrt[3]{16y}+9xy\cdot\sqrt[3]{128y^4}\)
11) \(12x^2\cdot\sqrt[5]{64x^7y^8}-y\cdot\sqrt[5]{486x^{17}y^3}\)
12) \(\sqrt[5]{128a^{18}b^3c^{12}}\)
13) \(\sqrt[3]{18x^7y^2}\cdot\sqrt[3]{3x^{14}y^5}\)
14) \(\sqrt[6]{16x^5y^{13}}\cdot\sqrt[6]{4x^3y^{21}z^9}\)
For Problems 15-17, complete the radicand (the expression under the radical) that creates a true statement.
15) \(\sqrt[3]{9x^5y}\cdot\sqrt[3]{?}=3x^2y^3\)
16) \(\sqrt[4]{2x^{13}y^{19}}\cdot\sqrt[4]{?}=2\left|x^5y^7\right|\)
17) \(\sqrt[4]{4x^6y^{18}}\cdot\sqrt[4]{?}=2\left|x^3y^5\right|\cdot\sqrt[4]{3xy^3}\)
Review
Simplify each expression in the real numbers.
18) \(3x^2(4x^2y^{\frac{1}{3}})^0\)
19) \(\left(\frac{5\strut^{\frac{7}{10}}}{5\strut^{\frac{1}{5}}}\right)^{\small{6}}\)
Solution Bank
1) \(\sqrt[3]{54}\)
2) \(\sqrt[5]{96b^{15}}\)
3) \(\sqrt[4]{162x^{11}y^6}\)
4) \(\sqrt[4]{27x^3}\cdot \sqrt[4]{9x^2}\)
5) \(-11\sqrt[4]{12}\cdot 3\sqrt[4]{20}\)
6) \(\sqrt[3]{2a^{10}}\cdot \sqrt[3]{24a^4}\)
7) \(5\sqrt[3]{36x^{5}}\cdot 2\sqrt[3]{12x^{14}}\)
8) \(4\sqrt[6]{x}+13\sqrt[6]{x}\)
9) \(3\sqrt[4]{32}+\sqrt[4]{1250}\)
10) \(7x\cdot\sqrt[3]{54y^7}-5xy^2\cdot\sqrt[3]{16y}+9xy\cdot\sqrt[3]{128y^4}\)
11) \(12x^2\cdot\sqrt[5]{64x^7y^8}-y\cdot\sqrt[5]{486x^{17}y^3}\)
12) \(\sqrt[5]{128a^{18}b^3c^{12}}\)
13) \(\sqrt[3]{18x^7y^2}\cdot\sqrt[3]{3x^{14}y^5}\)
14) \(\sqrt[6]{16x^5y^{13}}\cdot\sqrt[6]{4x^3y^{21}z^9}\)
For Problems 15-17, complete the radicand (the expression under the radical) that creates a true statement.
15) \(\sqrt[3]{9x^5y}\cdot\sqrt[3]{?}=3x^2y^3\)
16) \(\sqrt[4]{2x^{13}y^{19}}\cdot\sqrt[4]{?}=2\left|x^5y^7\right|\)
17) \(\sqrt[4]{4x^6y^{18}}\cdot\sqrt[4]{?}=2\left|x^3y^5\right|\cdot\sqrt[4]{3xy^3}\)
Review
Simplify each expression in the real numbers.
18) \(3x^2(4x^2y^{\frac{1}{3}})^0\)
19) \(\left(\frac{5\strut^{\frac{7}{10}}}{5\strut^{\frac{1}{5}}}\right)^{\small{6}}\)
Solution Bank