Multiply by 7

Learning Objectives Apply the power of a power rule to expressions by multiplying the exponent by 7. Simplify complex expressions involving rational exponents where the base is 7 or a power of 7. Solve equations with rational exponents that require raising a term to the 7th power. Convert expressions between radical form (specifically the 7th root) and exponential form. Evaluate numerical expressions with rational exponents where a key step involves multiplying an exponent by 7. Analyze how multiplying a rational exponent by 7 transforms the value and structure of an algebraic expression. What is the 7th power of the 7th root of a number? 🤔 This lesson reveals how this simple-sounding question unlocks a powerful shortcut in advanced algebra! Welcome to a specialized look a...

TermDefinitionExample Rational ExponentAn exponent expressed as a fraction m/n, where 'm' represents the power and 'n' represents the root. The expression b^(m/n) is equivalent to the nth root of b raised to the mth power.The expression 8^(2/3) means 'the cube root of 8, squared'. So, (∛8)² = 2² = 4. Power of a Power RuleWhen raising a power to another power, you multiply the exponents.(x^3)^2 = x^(3*2) = x^6. In this lesson, we focus on cases like (x^(a/b))^7 = x^(7a/b). Base of 7An expression where the base number being raised to a power is 7.7^(1/2), which is the square root of 7. 7th RootA number that must be multiplied by itself 7 times to equal a given value. It is the inverse operation of raising to the 7th power.The 7th root of 128 is 2, because 2^7 =...

Power Rule with Multiplication by 7 (b^(m/n))^7 = b^((m/n) * 7) = b^(7m/n) Use this rule to simplify an expression where a base with a rational exponent is raised to the 7th power. You multiply the rational exponent by 7. Solving Equations with 7th Roots If x^(a/7) = c, then (x^(a/7))^(7/a) = c^(7/a), which simplifies to x = c^(7/a). To solve for a variable raised to a fractional exponent with 7 in the denominator, raise both sides of the equation to the reciprocal power. This often involves multiplying the existing exponent by 7.