Use Mathematical Induction to Prove the Given Statement for All $$\left( \frac { x } { y } \right) ^ { n } = \frac { x ^ { n } } { y ^ { n } } \text { provided that } \mathrm { y } \neq 0$$

question 127

Short Answer

Use mathematical induction to prove the given statement for all positive integers n and real numbers x
and y.
- $$\left( \frac { x } { y } \right) ^ { n } = \frac { x ^ { n } } { y ^ { n } } \text { provided that } \mathrm { y } \neq 0$$

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Definitions:

Hot Magma

Molten or partially molten rock beneath the Earth's surface, from which igneous rocks are formed.

Subduction

Subduction is a geological process in which one tectonic plate moves under another plate and into the mantle as the plates converge, typically occurring at oceanic trenches.

Juan de Fuca Ridge

A tectonic plate boundary located off the coast of the Pacific Northwest region of North America, characterized by seafloor spreading and volcanic activity.

Hot Spot

A region with significantly higher temperature than its surroundings, often related to volcanic activity or environmental anomalies.