Which of the following is equal to $7^{1 / 3}$?
A. $\sqrt{7 \cdot 3}$
B. $\sqrt{7}$
C. $\sqrt[3]{7}$
D. $7^3$
Answer (2)
The problem requires identifying the expression equivalent to 7 1/3 .
Option A, 7 × 3 , simplifies to ( 21 ) 1/2 , which is not equal to 7 1/3 .
Option B, 7 , simplifies to 7 1/2 , which is not equal to 7 1/3 .
Option C, 3 7 , simplifies to 7 1/3 , which matches the given expression. Therefore, the answer is C .
Explanation
Understanding the problem We are asked to find which of the given options is equal to 7 1/3 . Let's analyze each option.
Analyzing option A Option A: 7 × 3 = 21 = ( 21 ) 1/2 . This is not equal to 7 1/3 .
Analyzing option B Option B: 7 = 7 1/2 . This is not equal to 7 1/3 .
Analyzing option C Option C: 3 7 = 7 1/3 . This matches the given expression.
Analyzing option D Option D: 7 3 = 7 × 7 × 7 = 343 . This is not equal to 7 1/3 .
Conclusion Therefore, the correct answer is C. 3 7 = 7 1/3 .
Examples
Understanding fractional exponents like 7 1/3 is crucial in various fields. For instance, in finance, it helps calculate growth rates over different periods. If an investment grows by a factor of 7 over 3 years, the annual growth rate can be found using 7 1/3 , which represents the cube root of 7. This concept extends to other areas like physics, where it can be used to determine relationships between quantities that scale non-linearly, such as volume and radius of a sphere.
The expression 7 1/3 is equivalent to C. √[3] 7 . Analyzing the other options shows that they do not equal 7 1/3 . Thus, C is the correct answer.
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