What Is The Power Of A Power Rule For Exponents The power of a quotient rule of exponents is used to find the result of a quotient that is raised to an exponent This law says quot Distribute the exponent to both the numerator and the denominator quot Here the bases are different and the exponents are the same for both the bases
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 Exponents and Powers The expression of repeated multiplication of a factor is power Exponent represents the number of times a factor is multiplied to itself Learn in detail at BYJU S
What Is The Power Of A Power Rule For Exponents
What Is The Power Of A Power Rule For Exponents
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The Power Rule for Exponents For any positive number x and integers a and b latex left x a right b x a cdot b latex Take a moment to contrast how this is different from the product rule for exponents found on the previous page The Power Rule for Powers The following examples suggest a rule for raising a power to a power Using the product rule we get Power Rule for Powers If is a real number and and are natural numbers To raise a power to a power multiply the exponents
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 8 215 8 64 In words 8 2 could be called quot 8 to the second power quot quot 8 to the power 2 quot or simply quot 8 squared quot Try it yourself Aug 9 2024 nbsp 0183 32 The power of a power exponent rule is a useful law of exponents that you can use to simplify complicated expressions involving multiple exponents
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RULE 5 Power of a Power Property of Exponent When an exponential expression is raised to a power copy the base which is a nonzero real number then multiply the inner and outer exponents We assume here that latex b ne 0 latex and both m and n are integers Nov 14 2021 nbsp 0183 32 Since 3x 2 is raised to the power of zero then we can apply the zero power rule begin array rl 3x 2 0 amp text Zero power rule 1 amp text Simplified expression end array nonumber
Power of a power 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 begin gather x a b x ab label power power end gather 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
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What Is The Power Of A Power Rule For Exponents - The Power Rule for Exponents For any positive number x and integers a and b latex left x a right b x a cdot b latex Take a moment to contrast how this is different from the product rule for exponents found on the previous page