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### Math

## Common Core Math

# High School: Number and Quantity: The Real Number System

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

- 4th & 5th roots
- Equivalent forms of exponential expressions
- Equivalent forms of exponential expressions
- Evaluate radical expressions challenge
- Evaluating fractional exponents
- Evaluating fractional exponents: fractional base
- Evaluating fractional exponents: negative unit-fraction
- Evaluating mixed radicals and exponents
- Evaluating quotient of fractional exponents
- Properties of exponents (rational exponents)
- Properties of exponents intro (rational exponents)
- Rewrite exponential expressions
- Rewriting exponential expressions as A⋅Bᵗ
- Rewriting mixed radical and exponential expressions
- Rewriting quotient of powers (rational exponents)
- Simplify square roots
- Simplify square roots (variables)
- Simplify square-root expressions
- Simplifying cube root expressions
- Simplifying cube root expressions (two variables)
- Simplifying higher-index root expressions
- Simplifying higher-index roots
- Simplifying square roots
- Simplifying square roots (variables)
- Simplifying square roots review
- Simplifying square-root expressions
- Solve exponential equations using exponent properties
- Solve exponential equations using exponent properties (advanced)
- Solving exponential equations using exponent properties
- Solving exponential equations using exponent properties (advanced)

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

- Proof: √2 is irrational
- Proof: product of rational & irrational is irrational
- Proof: square roots of prime numbers are irrational
- Proof: sum & product of two rationals is rational
- Proof: sum of rational & irrational is irrational
- Proof: there's an irrational number between any two rational numbers
- Rational vs. irrational expressions
- Sums and products of irrational numbers
- Worked example: rational vs. irrational expressions
- Worked example: rational vs. irrational expressions (unknowns)