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# Laws of exponents and examples of two laws of exponents

Laws of Exponents
The same laws hold for rational-number exponents as for integer exponents.
We list them for review.
For any real number a and any rational exponents m and n:
1. In multiplying, we can add exponents if the
bases are the same.
2. In dividing, we can subtract exponents if the
bases are the same.
3. To raise a power to a power, we can multiply
the exponents.
4. To raise a product to a power, we can raise
each factor to the power.
5. To raise a quotient to a power, we can raise
both the numerator and the denominator to
the power.

Provide an example of two of the laws of exponents. Explain how to simplify them. Tell how do the laws work with rational exponents and then provide a third example to simplify that includes a rational (fractional) exponent.

#### Solution Preview

Let us take the example of the law In multiplying, we can add exponents if the
bases are the same

x^2 ...

#### Solution Summary

Detailed solution is provided.

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