Multiply by 12

Learning Objectives Apply the properties of rational exponents to simplify complex terms before multiplying by 12. Correctly multiply monomials and polynomials containing rational exponents by the constant 12. Evaluate numerical expressions involving rational exponents that are multiplied by 12, including those with negative exponents. Distinguish between multiplying a coefficient by 12 and incorrectly multiplying a base by 12. Convert expressions between radical and rational exponent form to simplify problems involving multiplication by 12. Solve multi-step problems where multiplying by 12 is a key step in simplifying a larger expression with rational exponents. How can multiplying by a simple number like 12 test our mastery of advanced exponents? Let's find out! 🧐 T...

TermDefinitionExample Rational ExponentAn exponent expressed as a fraction m/n, where 'm' represents the power and 'n' represents the root.x^(2/3) means the cube root of x squared, or (∛x)². BaseThe number or variable that is being raised to a power in an exponential expression.In the expression 12 * (5x)^(3/4), the base of the exponent is 5x. CoefficientA numerical or constant quantity placed before and multiplying the variable in an algebraic expression.In the term 7x^(1/2), the coefficient is 7. When we multiply by 12, we are changing the term's coefficient: 12 * 7x^(1/2) = 84x^(1/2). Radical FormA way of writing an expression using a root symbol (√). It is an alternative to using a rational exponent.The expression x^(1/2) in radical form is √x. Order of Operat...

The Rational Exponent Rule a^(m/n) = (ⁿ√a)ᵐ = ⁿ√(aᵐ) This rule defines how to interpret a rational exponent. You can either take the nth root first and then apply the mth power, or apply the mth power first and then take the nth root. This is the first step in simplifying a term before you multiply by 12. Product of Powers Property xᵃ ⋅ xᵇ = xᵃ⁺ᵇ When multiplying like bases, add the exponents. This is often used to combine terms before multiplying the entire expression by 12. Power of a Power Property (xᵃ)ᵇ = xᵃᵇ When raising a power to another power, multiply the exponents. This is crucial for simplifying expressions like (8x⁹)^(1/3) before you multiply by 12. Distributive Property c(a + b) = ca + cb This property is used when you multiply a polynomial by 12...