Which of the following is equivalent to (5)^7/3

But before we dive in, let’s recall the rules of exponentiation.

When we have a fractional exponent, such as 7/3, we can rewrite it as a combination of a whole number exponent and a root. In this case, we can express (5)^7/3 as (5^7)^(1/3).

Now, let’s simplify further. We know that (a^m)^(1/n) = a^(m/n). Applying this rule, we get (5^7)^(1/3) = 5^(7/3).

But here’s the interesting part: 5^(7/3) can also be written as (5^7)^(1/3) = ∛(5^7). This is because the cube root of a number is equivalent to raising that number to the power of 1/3.

So, to summarize:

(5)^7/3 = 5^(7/3) = ∛(5^7)

All three expressions are equivalent, and each one offers a unique perspective on the power of exponentiation. Whether you’re a math whiz or just starting to explore the world of exponents, we hope this explanation has shed some light on the mysteries of (5)^7/3.