Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

if you got: f and g n now find: rewrite $x^{\\frac{6}{7}}$ as a root

Question

if you got:
f and g
n
now find:
rewrite $x^{\frac{6}{7}}$ as a root

Explanation:

Step1: Recall exponent - root rule

The rule for converting a fractional exponent to a root is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (where \(n\gt0\), \(a\) is a real number, and \(m,n\) are integers).

Step2: Apply the rule to \(x^{\frac{6}{7}}\)

Here, \(a = x\), \(m = 6\), and \(n=7\). Using the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), we substitute the values: \(x^{\frac{6}{7}}=\sqrt[7]{x^{6}}\).

Answer:

\(\sqrt[7]{x^{6}}\)