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The power of a power rule is an important exponent rule (law of exponent) used to simplify an expression of the form $(x^{m})^{n}$, where the base x is raised to a power m and the entire expression $x^{m}$ is raised to the power n again.
The power of a power rule in exponents is a rule that is applied to simplify an algebraic expression when a base is raised to a power, and then the whole expression is raised to another power. Before we get into the detail of the concept, let us recall the meaning of power and base.
We can raise exponential to another power, or take a power of a power. The result is a single exponential where the power is the product of the original exponents: (xa)b = xab. We can see this result by writing it as a product where the xa is repeated b times: (xa)b = xa × xa × ⋯ × xa ⏟ b times.
The 'power of a product rule of exponents' is used to find the result of a product that is raised to an exponent. This law says, "Distribute the exponent to each multiplicand of the product." Here is an example.
18 lip 2022 · Definition: The Power of a Quotient Rule for Exponents. For any real number a a and b b and any integer n n, the power of a quotient rule for exponents is the following: (a b)n = an bn (a b) n = a n b n, where b ≠ 0 b ≠ 0. Simplify the following using power of a quotient rule for exponents.
12 lis 2017 · Here is a graphic organizer that contains all the power rules for exponents. Rationale of Fractional Powers. In the section above, called Fractional Powers, we saw how fractional powers are related to radical expressions. This section will explain why that relation is true.
The power of a power rule tells us that when we have an exponential expression raised to a power, we simply have to copy the base and multiply the exponents. Here, we assume that the base is nonzero and that the exponents are integers: Power of a power – Examples with answers.
