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Sonja [21]
3 years ago
9

How do i show that this equation equals this?

Mathematics
1 answer:
sladkih [1.3K]3 years ago
8 0

Answer:

See explanation below.

Step-by-step explanation:

So we will have to somehow show that \sqrt[x]{b^{m}} equals (\sqrt[x]{b})^{m} by using b^{\frac{m}{n}}.

\sqrt[x]{b^{m}}=(b^{m})^{\frac{1}{x}}=b^{m*\frac{1}{x}}=b^{\frac{m}{x}}

(\sqrt[x]{b})^{m}=(b^{\frac{1}{x}})^{m}=b^{m*\frac{1}{x}}=b^{\frac{m}{x}}

So we have shown that:

\sqrt[x]{b^{m}}=b^{\frac{m}{x}}

and

(\sqrt[x]{b})^{m}=b^{\frac{m}{x}}

So by the transitive property of equality:

\sqrt[x]{b^{m}}=(\sqrt[x]{b})^{m}

I hope you find my answer and explanation to be helpful. Happy studying. :D

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