1) Which of the expressions are not equivalent to \(\left(\sqrt[6]{64}\right)^{\small{5}}\)?
a) \(64\strut^{{\large\frac{5}{6}}}\)
b) \(\sqrt[5]{2^6}\)
c) \(32\)
d) \(2^5\)
e) \(16\strut^{\large\frac{5}{2}}\)
Simplify each expression in the real numbers.
2) \(27\strut^{-\large\frac{4}{3}}\)
3) \(9\strut^{\large\frac{5}{2}}\)
4) \((-16)\strut^{\large\frac{7}{4}}\)
5) \(\Large{\frac{1}{125\strut^{-\normalsize{\frac{4}{3}}}}}\)
6) \(\left(\large\frac{9}{16}\right)^{-\large\frac{3}{2}}\)
7) \((25)\strut{^{-\large\frac{1}{2}}}\)
8) \((-27)^{\frac{2}{3}}\)
9) \((-8)\strut{^{\large\frac{5}{3}}}\)
10) \(\left(\large\frac{81}{625}\right)^{\large\frac{3}{4}}\)
11) \(\large{\frac{25\strut^{\large\frac{3}{4}}}{25\strut^{\large\frac{1}{4}}}}\)
12) \(\left(27^{\large\frac{2}{5}}\right)^{\large\frac{5}{3}}\)
13) \(\Large{\frac{8}{8\strut^{\normalsize{\frac{10}{3}}}}}\)
14) \(x\strut^{\large\frac{9}{10}} \cdot x\strut^{\large\frac{3}{10}}\)
15) \(\Large{\frac{x\strut^{\normalsize{\frac{3}{4}}}}{x\strut^{\normalsize{\frac{15}{4}}}}}\)
16) \(\left(6^6\cdot x\strut^{\large\frac{2}{3}}\right)^{\large\frac{1}{3}}\)
17) \(-2x\strut^{\large\frac{1}{2}}\cdot4x\strut^{\large\frac{3}{2}}\)
18) \(\Large{\frac{3x\strut^{\frac{1}{5}}}{9x\strut^{\frac{1}{2}}}}\)
19) \(\large\frac{1}{4}\normalsize{x}\strut^{-\large\frac{2}{7}}\cdot\normalsize{16x}\strut^{\large\frac{3}{2}}\)
20) \(\left(81x\strut^{\frac{2}{3}}\right)^{\frac{3}{4}}\)
21) \(\left(9x^{16}\right)^{-\frac{1}{2}}\)
22) \(\left(8x\strut^{\frac{1}{2}}\right)^{\frac{2}{3}}\cdot \left(25x\strut^{\frac{4}{3}}\right)^{\frac{1}{2}}\)
23) \(\left(16x^4\right)^{-\frac{3}{2}}\cdot \left(8x^{12}\right)^{\frac{4}{3}}\)
24) \(\Large{\frac{7x\strut^{\frac{5}{2}}y\strut^{-\frac{2}{3}}}{28xy\strut^{\frac{1}{6}}}}\)
25) \(\Large{\frac{30x\strut^{\frac{7}{12}}y^4}{45x\strut^{-\frac{5}{6}}y\strut^{\frac{11}{3}}}}\)
Solution Bank
a) \(64\strut^{{\large\frac{5}{6}}}\)
b) \(\sqrt[5]{2^6}\)
c) \(32\)
d) \(2^5\)
e) \(16\strut^{\large\frac{5}{2}}\)
Simplify each expression in the real numbers.
2) \(27\strut^{-\large\frac{4}{3}}\)
3) \(9\strut^{\large\frac{5}{2}}\)
4) \((-16)\strut^{\large\frac{7}{4}}\)
5) \(\Large{\frac{1}{125\strut^{-\normalsize{\frac{4}{3}}}}}\)
6) \(\left(\large\frac{9}{16}\right)^{-\large\frac{3}{2}}\)
7) \((25)\strut{^{-\large\frac{1}{2}}}\)
8) \((-27)^{\frac{2}{3}}\)
9) \((-8)\strut{^{\large\frac{5}{3}}}\)
10) \(\left(\large\frac{81}{625}\right)^{\large\frac{3}{4}}\)
11) \(\large{\frac{25\strut^{\large\frac{3}{4}}}{25\strut^{\large\frac{1}{4}}}}\)
12) \(\left(27^{\large\frac{2}{5}}\right)^{\large\frac{5}{3}}\)
13) \(\Large{\frac{8}{8\strut^{\normalsize{\frac{10}{3}}}}}\)
14) \(x\strut^{\large\frac{9}{10}} \cdot x\strut^{\large\frac{3}{10}}\)
15) \(\Large{\frac{x\strut^{\normalsize{\frac{3}{4}}}}{x\strut^{\normalsize{\frac{15}{4}}}}}\)
16) \(\left(6^6\cdot x\strut^{\large\frac{2}{3}}\right)^{\large\frac{1}{3}}\)
17) \(-2x\strut^{\large\frac{1}{2}}\cdot4x\strut^{\large\frac{3}{2}}\)
18) \(\Large{\frac{3x\strut^{\frac{1}{5}}}{9x\strut^{\frac{1}{2}}}}\)
19) \(\large\frac{1}{4}\normalsize{x}\strut^{-\large\frac{2}{7}}\cdot\normalsize{16x}\strut^{\large\frac{3}{2}}\)
20) \(\left(81x\strut^{\frac{2}{3}}\right)^{\frac{3}{4}}\)
21) \(\left(9x^{16}\right)^{-\frac{1}{2}}\)
22) \(\left(8x\strut^{\frac{1}{2}}\right)^{\frac{2}{3}}\cdot \left(25x\strut^{\frac{4}{3}}\right)^{\frac{1}{2}}\)
23) \(\left(16x^4\right)^{-\frac{3}{2}}\cdot \left(8x^{12}\right)^{\frac{4}{3}}\)
24) \(\Large{\frac{7x\strut^{\frac{5}{2}}y\strut^{-\frac{2}{3}}}{28xy\strut^{\frac{1}{6}}}}\)
25) \(\Large{\frac{30x\strut^{\frac{7}{12}}y^4}{45x\strut^{-\frac{5}{6}}y\strut^{\frac{11}{3}}}}\)
Solution Bank