Multiply by 8

Learning Objectives Represent the number 8 as a power of its prime base, 2. Apply the product rule of exponents to simplify expressions involving multiplication by 8. Add rational exponents with both common and uncommon denominators. Simplify algebraic expressions containing rational exponents and coefficients that are powers of 2. Evaluate numerical expressions with rational exponents that result from multiplying by 8. Convert simplified expressions between exponential and radical forms. Solve equations involving a variable term with a rational exponent that is multiplied by 8. Ever thought multiplying by 8 could be an advanced algebra skill? 🤯 Let's see how this simple number unlocks complex problems in the world of rational exponents! This tutorial will show you...

TermDefinitionExample Rational ExponentAn exponent that is a fraction, in the form m/n, where m is the power and n is the root.In the expression 27^(2/3), the rational exponent is 2/3. This means 'take the cube root of 27, then square the result': (∛27)² = 3² = 9. BaseThe number or variable that is being raised to a power.In the expression 2^(5/2), the base is 2. Exponential FormA way of representing a number using a base and an exponent.The number 8 can be written in exponential form with a base of 2 as 2³. Radical FormA way of representing a number using a radical symbol (√).The expression x^(1/2) in radical form is √x. Product Rule of ExponentsWhen multiplying two expressions with the same base, you keep the base and add the exponents.x⁵ * x² = x^(5+2) = x⁷. Power of a Power...

The Power of 8 8 = 2³ The foundational step for this topic. To apply exponent rules when multiplying by 8, you must first express 8 as a power of its prime base, 2. Product Rule for Rational Exponents b^(m/n) * b^(p/q) = b^((m/n) + (p/q)) When multiplying expressions that share a common base, you add their rational exponents. This requires finding a common denominator for the fractions. Definition of a Rational Exponent x^(m/n) = (ⁿ√x)ᵐ = ⁿ√(xᵐ) This rule connects exponential form to radical form. It is used to interpret the final answer or to evaluate numerical expressions.