Answer:
Step-by-step explanation:
[tex]\sqrt[4]{(16a^4)^5}=(16a^4)^{\frac{5}{4}}[/tex] [Since, [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]]
[tex]=(16)^{\frac{5}{4}}(a^4)^{\frac{5}{4}}[/tex]
[tex]=(2^4)^{\frac{5}{4}}(a^4)^{\frac{5}{4} }[/tex]
[tex]=(2^{4\times \frac{5}{4}})(a^{4\times \frac{5}{4}})[/tex]
[tex]=2^5a^5[/tex]
[tex]\sqrt[5]{(b^{\frac{1}{4}})^6}=\sqrt[5]{b^{\frac{6}{4}}}[/tex]
[tex]=\sqrt[5]{b^{\frac{3}{2}}}[/tex]
[tex]=(b^{\frac{3}{2}})^{\frac{1}{5} }[/tex]
[tex]=b^{\frac{3}{10}}[/tex]
[tex]\sqrt[3]{\frac{c^{15}}{c^9}}=\sqrt[3]{c^{15-9}}[/tex]
[tex]=(c^6)^{\frac{1}{3}}[/tex]
[tex]=c^{6\times \frac{1}{3} }[/tex]
= c²
[tex]\sqrt[4]{16d^6\times 16d^{-5}}=\sqrt[4]{(2)^4(d^{6-5})(2)^4}[/tex]
[tex]=\sqrt[4]{2^{(4+4)}d}[/tex]
[tex]=\sqrt[4]{(2^8)d}[/tex]
[tex]=2^{\frac{8}{4}}d^{\frac{1}{4}}[/tex]
[tex]=2^2d^{\frac{1}{4}}[/tex]
[tex]=4d^{\frac{1}{4}}[/tex]