Question

The seventh root of x divided by the eighth root of x is
A. x
B.
C.
D.

Answer 1

The seventh root of x divided by the eighth root of x is fifty sixth root of x

Step-by-step explanation:

Given that " The seventh root of x divided by the eighth root of x "

It can be written as $\frac{\sqrt[7]{x}}{\sqrt[8]{x}}$

To find the value of the given expression :

• First simplify the given expression
• $\frac{\sqrt[7]{x}}{\sqrt[8]{x}}$
• $=\frac{x^{\frac{1}{7}}}{x^{\frac{1}{8}}}$ ( here using the property $\sqrt[m]{a}=a^{\frac{1}{m}}$ )
• $=x^{\frac{1}{7}}\times x^{(-\frac{1}{8})}$ ( here using the property $a^{-m}=\frac{1}{a^m}$ )
• $=x^{\frac{8-7}{(7)(8)}$ ( taking LCM here )
• $=x^{\frac{1}{56}$
• $=\sqrt[56]{x}$ ( here using the property $a^{\frac{1}{m}}=\sqrt[m]{a}$ )
• $\frac{\sqrt[7]{x}}{\sqrt[8]{x}}=\sqrt[56]{x}$

Therefore the option $\sqrt[56]{x}$ is correct

The seventh root of x divided by the eighth root of x is fifty sixth root of x

Answer 2

Answer:

The seventh root of x divided by the eighth root of x is √ 56 .    

Step-by-step explanation: