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If b = 2^(1/3), what is b^6?
Practice Questions
Q1
If b = 2^(1/3), what is b^6?
4
8
16
32
Questions & Step-by-Step Solutions
If b = 2^(1/3), what is b^6?
Correct Answer: 4
Steps
Concepts
Step 1: Start with the value of b, which is given as b = 2^(1/3).
Step 2: We need to find b^6, so we write it as (2^(1/3))^6.
Step 3: Use the power of a power rule, which says (a^m)^n = a^(m*n). Here, a = 2, m = 1/3, and n = 6.
Step 4: Multiply the exponents: (1/3) * 6 = 6/3 = 2.
Step 5: Now we have (2^(1/3))^6 = 2^(2).
Step 6: Calculate 2^2, which equals 4.
Exponents
– Understanding how to manipulate exponents, including the power of a power rule.
Roots and Powers
– Recognizing the relationship between roots and their corresponding powers.
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