Algebraic roots & indices

• What is the topic of the study material?

  Algebraic Roots & Indices
• Can the laws of indices be used with algebraic terms?

  Yes, the laws of indices work with numerical and algebraic terms.
• How can you simplify expressions where terms are multiplied or divided?

  By dealing with the number and algebraic parts separately.

  
• What is the result of simplifying $3x^7 \times 6x^4$?


  The result is $18x^{11}$.
• What does $3x^7 \div 6x^4$ simplify to?


  It simplifies to $\frac{1}{2}x^3$.

  
• What is the result of $(3x^7)^2$?


  The result is $9x^{14}$.

  
• How can you solve equations when the unknown is in the index?

  If two powers are equal and the base numbers are the same, then the indices must be the same.
• What is the implication of the equation $a^x =$$a^y$?


  It implies that $x =$$y$.

  
• What should you do if the unknown is part of the index?

  You should write both sides with the same base number.
• How do you solve the equation $5^{2x} =$$125$?


  Rewrite it as $5^{2x} =$$5^3$ to find $2x =$$3$, thus $x =$$\frac{3}{2}$.

  
• How do you solve $8^x =$$1/4$?


  You rewrite it as $4^{-1} =$$2^{-2}$ to find $8^x =$$2^{-2}$.
• What is the process to solve $2^{3x} =$$2^{-2}$?


  Set the indices equal to each other: $3x =$$-2$, thus $x =$$-\frac{2}{3}$.
• What are the steps to simplify <latex>(3x^2)(2x^3y^2)/(6x^2y)

  1. Multiply out the brackets in the numerator.
  2. Rearrange the numerator to multiply numbers, terms, and variables together.
  3. Simplify the numerator.
  4. Multiply constants and add powers of the terms.
  5. Divide the constants.
  6. Subtract the power of the term in the denominator from the numerator.
  7. Simplify the expression.

  
• What are the steps to simplify <latex>\frac{54x^7}{2x^4} - \frac{1}{3}

  1. Simplify the expression inside the brackets.
  2. Cancel down the constants.
  3. Subtract the power of the term in the denominator from the numerator.
  4. Apply the negative index outside the brackets by flipping the fraction.
  5. Apply the fractional index outside the brackets to everything inside the brackets.

  
• Where can students find more resources for algebraic roots and indices?

  Students can visit www.savemyexams.com for more resources.