Question

Which of the following represents sixth root of x to the fifth power in exponential form?
5x6
6x5
x to the 5 sixths power
x to the 6 fifths power

Answer 1

x to the 5 sixth power

Answer 2

Answer:

$\sqrt[6]{x}=x^{\frac{5}{6}$

Option 3 is correct.

Step-by-step explanation:

$\text{Given the expression in words which represents sixth root of x to the fifth power }$

we have to write in exponential form.

Step 1: sixth root of x can be written as

$\sqrt[6]{x}=x^{\frac{1}{6}$

Step 2: Fifth power of sixth root of x

$(x^{\frac{1}{6})^5$

$\text{As, }(x^m)^n=x^{mn}$

$(x^{\frac{1}{6}})^5=x^{{5\times \frac{1}{6}}}=x^{\frac{5}{6}}$

which implies x to the 5 sixths power.

Option 3 is correct.