Answer:
Option d) 5 to the power of negative 5 over 6 is correct.
[tex]\dfrac{\sqrt[3]{\bf 5} \times \sqrt{\bf 5}}{\sqrt[3]{\bf 5^{\bf 5}}}= 5^{\frac{\bf -5}{\bf 6}}[/tex]
Above equation can be written as 5 to the power of negative 5 over 6.
ie, [tex]5^\frac{\bf -5}{\bf 6}[/tex]
Step-by-step explanation:
Given that cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5.
It can be written as below
[tex]\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}[/tex]
[tex] \dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{1}{3}} \times 5^{\frac{1}{2}}}{5^{\frac{5}{3}}}[/tex]
[tex]\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{1}{3}+\frac{1}{2}}}{5^{\frac{5}{3}}}[/tex]
[tex]\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{2+3}{6}}}{5^{\frac{5}{3}}}[/tex]
[tex]\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= 5^{\frac{5}{6}} \times 5^{\frac{-5}{3}}[/tex]
[tex]\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= 5^{\frac{5-10}{6}}[/tex]
[tex]\dfrac{\sqrt[3]{5} \times \sqrt{5}}{5^5}= 5^{\frac{-5}{6}}[/tex]
Above equation can be written as 5 to the power of negative 5 over 6.
