Difference between revisions of "Laws of Exponents for Real Numbers"
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== Laws of Exponents == | == Laws of Exponents == | ||
Let <math>a >0</math> be a real number and <math>p</math> & <math>q</math> be rational numbers. Then we have | Let <math>a >0</math> be a real number and <math>p</math> & <math>q</math> be rational numbers. Then we have | ||
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* <math>(a^p)^q=a^{pq}</math> | * <math>(a^p)^q=a^{pq}</math> | ||
* <math>\frac{a^p}{a^q}=a^{p-q}</math> | * <math>\frac{a^p}{a^q}=a^{p-q}</math> | ||
*<math>a^{-p}=\frac{1}{a^p}</math> | |||
*<math>a^\frac{1}{p}=\sqrt[p]{a}</math> | |||
*<math>a^0=1</math> | |||
== Examples == | |||
# <math>5^2 \times 5^5 = 5^{2+5}=5^7</math> | |||
# <math>(5^2)^3=5^{2 \times 3}=5^6</math> | |||
# <math>\frac{5^6}{5^4}=5^{6-4}=5^2 =25</math> | |||
# <math>5^{-2}=\frac{1}{5^2}=\frac{1}{25}</math> | |||
# <math>5^\frac{1}{3}=\sqrt[3]{5}</math> | |||
# <math>5^0=1</math> |
Latest revision as of 08:14, 30 April 2024
The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. In this article, we will be knowing the six important laws of exponents.
Laws of Exponents
Let be a real number and & be rational numbers. Then we have