For problems 1-5, Simplify:
1) \(\Large{\frac{x^{3a-7}}{x^{2a-5}}}\)
2) \(\Large\frac{\left(a^{2x+1}\right)^4}{\left(a^x\right)^7\left(a^{2x-3}\right)}\)
3) \(\Large{\left[\frac{\left(3x^{-4}y^5\right)^{-2}}{\left(3x^{-4}y^7\right)^{-3}}\right]^{-4}}\)
4) \(\large{\left(\frac{-5a\strut{^9}}{b\strut{^{-8}}}\right)^3\left(\frac{4b\strut{^7}ca\strut{^{-5}}}{3\strut{^{-1}}bc\strut{^6}}\right)^{-2}}\)
5) \(\large\left(x\strut{^{-\frac{4}{9}}}y\strut{^{\frac{2}{3}}}\right)^{-27}\left(x\strut{^{-9}}y\strut{^{-\frac{7}{10}}}\right)^{-\frac{5}{3}}\)
6) Solve: \(\large\left(\frac{16}{25}\right)^{\left(4-x\right)}=\Large{\frac{\left(\frac{64}{125}\right)^{\frac{3x}{5}}}{\left(\frac{4}{5}\right)^{-3}}}\)
Solution Bank
1) \(\Large{\frac{x^{3a-7}}{x^{2a-5}}}\)
2) \(\Large\frac{\left(a^{2x+1}\right)^4}{\left(a^x\right)^7\left(a^{2x-3}\right)}\)
3) \(\Large{\left[\frac{\left(3x^{-4}y^5\right)^{-2}}{\left(3x^{-4}y^7\right)^{-3}}\right]^{-4}}\)
4) \(\large{\left(\frac{-5a\strut{^9}}{b\strut{^{-8}}}\right)^3\left(\frac{4b\strut{^7}ca\strut{^{-5}}}{3\strut{^{-1}}bc\strut{^6}}\right)^{-2}}\)
5) \(\large\left(x\strut{^{-\frac{4}{9}}}y\strut{^{\frac{2}{3}}}\right)^{-27}\left(x\strut{^{-9}}y\strut{^{-\frac{7}{10}}}\right)^{-\frac{5}{3}}\)
6) Solve: \(\large\left(\frac{16}{25}\right)^{\left(4-x\right)}=\Large{\frac{\left(\frac{64}{125}\right)^{\frac{3x}{5}}}{\left(\frac{4}{5}\right)^{-3}}}\)
Solution Bank