Answer:
See explanation below.
Step-by-step explanation:
So we will have to somehow show that [tex]\sqrt[x]{b^{m}}[/tex] equals [tex](\sqrt[x]{b})^{m}[/tex] by using [tex]b^{\frac{m}{n}}[/tex].
[tex]\sqrt[x]{b^{m}}=(b^{m})^{\frac{1}{x}}=b^{m*\frac{1}{x}}=b^{\frac{m}{x}}[/tex]
[tex](\sqrt[x]{b})^{m}=(b^{\frac{1}{x}})^{m}=b^{m*\frac{1}{x}}=b^{\frac{m}{x}}[/tex]
So we have shown that:
[tex]\sqrt[x]{b^{m}}=b^{\frac{m}{x}}[/tex]
and
[tex](\sqrt[x]{b})^{m}=b^{\frac{m}{x}}[/tex]
So by the transitive property of equality:
[tex]\sqrt[x]{b^{m}}=(\sqrt[x]{b})^{m}[/tex]
I hope you find my answer and explanation to be helpful. Happy studying. :D
