Algebraic expressions (Part 2): ExponentsDIVIDING POWERSThere is a missing number in the following equation. It is represented by the blue diamond, ⧫⧫. Determine the value of this missing number.(p2)2(p3)⧫=1p5(𝑝2)2(𝑝3)⧫=1𝑝5Answer:The value of the missing number is: .2 attempts remaining
Question
Algebraic expressions (Part 2): ExponentsDIVIDING POWERSThere is a missing number in the following equation. It is represented by the blue diamond, ⧫⧫. Determine the value of this missing number.(p2)2(p3)⧫=1p5(𝑝2)2(𝑝3)⧫=1𝑝5Answer:The value of the missing number is: .2 attempts remaining
Solution
The problem is asking to find the value of the blue diamond, ⧫⧫, in the equation (p^2)^2 * (p^3)^⧫ = 1/p^5.
Step 1: Simplify the left side of the equation.
When you raise a power to a power, you multiply the exponents. So, (p^2)^2 becomes p^4.
So, the equation now reads: p^4 * (p^3)^⧫ = 1/p^5.
Step 2: Use the rule of exponents that says when you multiply powers with the same base, you add the exponents.
So, the left side of the equation becomes p^(4+3⧫) = 1/p^5.
Step 3: Use the rule of exponents that says when you divide powers with the same base, you subtract the exponents.
So, the equation becomes 4+3⧫ = -5.
Step 4: Solve for ⧫.
Subtract 4 from both sides to get 3⧫ = -9.
Then, divide both sides by 3 to get ⧫ = -3.
So, the value of the missing number is -3.
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