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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.
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 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.
Power to a Power — Rules & Examples. Practice. Explanations (3) Caroline K. Text. 8. Power Rule for Exponents. How do you raise a power to a power? Image by Caroline Kulczycky. In this formula, a, b, and x are all real numbers. We plug in values for each number and simplify. This is an example of using the order of operations.
18 lip 2022 · Definition: The Power of a Product Rule for Exponents. For any real number a and b and any number n, the power of a product rule for exponents is the following: (a ⋅ b)n = an ⋅ bn (a ⋅ b) n = a n ⋅ b n.
14 lis 2021 · \[\begin{array}{rl}\left(\dfrac{a^3b^{\color{blue}{1}}\color{black}{}}{c^8d^5}\right)^2&\text{Apply the power of a quotient rule} \\ \dfrac{a^{3\cdot 2}b^{1\cdot 2}}{c^{8\cdot 2}d^{5\cdot 2}}&\text{Multiply exponents} \\ \dfrac{a^6b^2}{c^{16}d^{10}}&\text{Simplified expression}\end{array}\nonumber\]
Exponent rules are those laws that are used for simplifying expressions with exponents. Learn about exponent rules, the zero rule of exponent, the negative rule of exponent, the product rule of exponent, and the quotient rule of exponent with the solved examples, and practice questions.
