If a^3 * b^2 = 64 and a = 2, what is the value of b? (2023)

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Question: If a^3 * b^2 = 64 and a = 2, what is the value of b? (2023)

Options:

Correct Answer: 8

Exam Year: 2023

Solution:

Substituting a = 2, we have 2^3 * b^2 = 64, which simplifies to 8b^2 = 64. Thus, b^2 = 8, leading to b = 4.

If a^3 * b^2 = 64 and a = 2, what is the value of b? (2023)

If a^3 * b^2 = 64 and a = 2, what is the value of b? (2023)

Step 1: Start with the equation a^3 * b^2 = 64.
Step 2: Substitute the value of a, which is 2, into the equation. This gives us 2^3 * b^2 = 64.
Step 3: Calculate 2^3. This equals 8, so now we have 8 * b^2 = 64.
Step 4: To isolate b^2, divide both sides of the equation by 8. This gives us b^2 = 64 / 8.
Step 5: Calculate 64 / 8. This equals 8, so now we have b^2 = 8.
Step 6: To find b, take the square root of both sides. This gives us b = √8.
Step 7: Simplify √8. This can be written as 2√2, but for the purpose of this problem, we can also find the approximate value, which is about 2.83.

Algebraic Manipulation – The question tests the ability to substitute values into an equation and solve for an unknown variable.
Exponents – Understanding how to work with exponents is crucial, as the equation involves powers of variables.