1.1.4 Working with powers and roots

• What is the cube root of 8?

  2
• What is the opposite of powers?

  Roots
• What is the side length of a square garden with an area of 36 square meters?

  6 meters
• Steps to evaluate 2³

  1️⃣ Identify the base as 2

  2️⃣ Identify the exponent as 3

  3️⃣ Multiply the base by itself 3 times: 2 x 2 x 2

  4️⃣ Calculate the result: 8
• What is the purpose of the rules of exponents?

  To simplify powers
• What should you do with the exponents when dividing powers with the same base?

  Subtract them
• Match the root with its example:

  Square Root ↔️ √25 = 5

  Cube Root ↔️ ∛8 = 2
• What is the formula for raising a power to another power?

  (a^m)^n = a^(m*n)
• Match the term with its definition:

  Coefficient ↔️ The number in front of a variable

  Exponent ↔️ The power to which a variable is raised

  Same Base ↔️ Variables raised to different powers
• What does the exponent in a power indicate?

  Number of multiplications
• Steps for simplifying exponents using the rules

  1️⃣ Identify the operation (addition, subtraction, multiplication, division)

  2️⃣ Apply the corresponding exponent rule

  3️⃣ Simplify the resulting expression
• What is the combined area of two squares with side length x?

  x^4
• What is a square root?

  A number multiplied by itself
• Steps for simplifying expressions with powers:

  1️⃣ Combine coefficients

  2️⃣ Add exponents of variables with the same base
• What is the value of 3²?

  9
• 5¹ is equal to 1

  False
• What is the area of a square with sides of 4 meters?

  16 square meters
• What operation is the opposite of raising a number to a power?

  Square root
• What does simplifying expressions with powers involve?

  Combining terms with same base
• What is the value of 5¹?

  5
• What is the area of a square with sides of 9 meters?

  81 square meters
• Match the base, exponent, and result:

  3 ↔️ 3² = 9

  4 ↔️ 4³ = 64

  5 ↔️ 5¹ = 5
• How do powers help in finding the area or volume of shapes?

  They simplify calculations
• Steps for calculating powers of numbers

  1️⃣ Identify the base

  2️⃣ Identify the exponent

  3️⃣ Multiply the base by itself the number of times indicated by the exponent

  4️⃣ Calculate the result
• Match the concept with its definition:

  Cube Root ↔️ The number multiplied twice

  Perfect Cube ↔️ Number with whole cube root
• What is the square root of 25?

  5
• Match the index law with its formula:

  Product Rule ↔️ a^m * a^n = a^(m+n)

  Quotient Rule ↔️ a^m / a^n = a^(m-n)

  Power of a Power Rule ↔️ (a^m)^n = a^(m*n)
• In a real-life scenario, if a colony of bacteria doubles every hour, how many times larger is the colony after three hours?

  8 times
• What is the formula to find the area of a square?

  Side²
• Why is the square root of 25 equal to 5?

  Because 5 x 5 = 25
• Why is the cube root of 8 equal to 2?

  2 x 2 x 2 =8
• What is √a expressed as a fractional exponent?

  $a^{\frac{1}{2}}$
• What is a cube root?

  A number multiplied twice
• What are index laws used for?

  Simplifying expressions involving powers
• What is (a^m)^n simplified using index laws?

  $a^{m \cdot n}$
• What is the power of a power rule?

  (a^m)^n = a^(m*n)
• Steps to calculate a square root

  1️⃣ Identify the number under the square root symbol.

  2️⃣ Find a number that, when multiplied by itself, equals the number.
• Steps to simplify x² * √x

  1️⃣ Convert √x to x^(1/2)

  2️⃣ Multiply x² by x^(1/2)

  3️⃣ Add the exponents: 2 + 1/2

  4️⃣ Simplify to x^(5/2)
• The expression x² * √x can be used to calculate the new area when doubling the side length of a square.

  False
• Steps to solve the example problem of finding the side length of a square with a given area

  1️⃣ Identify the formula: Side = √Area

  2️⃣ Calculate: Side = √121

  3️⃣ Find the square root: Side = 11 meters