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The power to the power rule states that 'If the base raised to a power is being raised to another power, then the two powers are multiplied and the base remains the same.' The formula for the power of a power rule is (a m ) n = a m n .
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.
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.
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.
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.
Exponents are also called Powers or Indices. The exponent of a number says how many times to use the number in a multiplication. In this example: 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared" Try it yourself: So an Exponent saves us writing out lots of multiplies! Example: a7.
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.
