Rational Exponents and Radical Expressions
02.01 Lesson Summary
To achieve mastery of this lesson, make sure that you develop responses to the essential question listed below.
How can an expression written in either radical form or rational exponent form, be rewritten to fit the other form?
The number inside the radical is the numerator and the number outside the radical sign is the denominator in the rational exponent form, if thats right then you just do the same thing with the exponent to find the radical form. Or by by recalling the rule
Rational Exponents Radical Expressions
The numerator of the rational exponent becomes the exponent on the radicand.
The denominator of the rational exponent becomes the index, or root, of the radical.
Radical Expressions Rational Exponents
The exponent on the radicand becomes the numerator of the rational exponent. The index, or root, of the radical becomes the denominator of the rational exponent.
02.02 Lesson Summary
To achieve mastery of this lesson, make sure that you develop responses to the essential question listed below:
How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents? you must not only apply the properties of radicals, but also remove any perfect nth powers (other than 1) and rationalize any denominators.
Product Property
When multiplying two of the same variable, the exponents are added. Fractions must have common denominators before being added or subtracted. d2/5 * d1/2 = d4/10* d5/10=d9/10
Quotient Property
When dividing two of the same variable, the exponents are subtracted. Fractions must have been common denominators before being added or subtracted b 5/6 over b ¼ = b 10/12 – 3/12= b7/12.
Negative Exponents
When simplifying negative exponents, take the reciprocal of the expression and make the exponent positive. m−3= 1/m^3
1/c-4=1/1/c^4=1 divide1/c^4=c4
02.03 Lesson Summary
To achieve mastery of this lesson, make sure that you develop responses to the essential questions
To achieve mastery of this lesson, make sure that you develop responses to the essential question listed below.
How can an expression written in either radical form or rational exponent form, be rewritten to fit the other form?
The number inside the radical is the numerator and the number outside the radical sign is the denominator in the rational exponent form, if thats right then you just do the same thing with the exponent to find the radical form. Or by by recalling the rule
Rational Exponents Radical Expressions
The numerator of the rational exponent becomes the exponent on the radicand.
The denominator of the rational exponent becomes the index, or root, of the radical.
Radical Expressions Rational Exponents
The exponent on the radicand becomes the numerator of the rational exponent. The index, or root, of the radical becomes the denominator of the rational exponent.
02.02 Lesson Summary
To achieve mastery of this lesson, make sure that you develop responses to the essential question listed below:
How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents? you must not only apply the properties of radicals, but also remove any perfect nth powers (other than 1) and rationalize any denominators.
Product Property
When multiplying two of the same variable, the exponents are added. Fractions must have common denominators before being added or subtracted. d2/5 * d1/2 = d4/10* d5/10=d9/10
Quotient Property
When dividing two of the same variable, the exponents are subtracted. Fractions must have been common denominators before being added or subtracted b 5/6 over b ¼ = b 10/12 – 3/12= b7/12.
Negative Exponents
When simplifying negative exponents, take the reciprocal of the expression and make the exponent positive. m−3= 1/m^3
1/c-4=1/1/c^4=1 divide1/c^4=c4
02.03 Lesson Summary
To achieve mastery of this lesson, make sure that you develop responses to the essential questions