Степень с рациональным показателем. Простейшие задачи
a12+13−16=a3+2−16=a46=a23a raised to the one-half plus one-third minus one-sixth power equals a raised to the the fraction with numerator 3 plus 2 minus 1 and denominator 6 end-fraction power equals a raised to the four-sixths power equals a raised to the two-thirds power Organizational Moment (2 min): Goal setting. Mental Math / Review (5 min): Reviewing -th degree roots. The laws governing rational exponents are identical to
The laws governing rational exponents are identical to those for integer exponents. For , and rational numbers Division: Power of a Power: Power of a Product: Power of a Quotient: 3. Practical Application & Task Examples establish its properties
To define a power with a rational exponent, establish its properties, and develop skills in simplifying expressions containing fractional exponents. 1. Theoretical Foundation The laws governing rational exponents are identical to
amn=amna raised to the m over n end-fraction power equals the n-th root of a to the m-th power end-root Note that must be greater than zero ( ). If the exponent is positive ( can also be zero. 2. Properties of Rational Exponents
By Grade 11, students are familiar with integer exponents. The transition to rational exponents introduces the relationship between powers and roots. For any and a rational number is an integer and is a natural number ), the power is defined as:
Solving problems from the textbook or Interneturok.