Question

Express the following fraction in simplest form using only positive exponents.

4(k^2)^4/12k^7
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Answer 1

We can simplify the expression in the numerator first.

4(k^2)^4 = 4(k^(2*4)) = 4(k^8)

Now we can substitute this into the original expression:

4(k^2)^4/12k^7 = 4(k^8)/12k^7

Simplifying further, we can cancel out a factor of 4 and simplify the denominator:

4(k^8)/12k^7 = (k^8)/(3k^7)

Finally, we can simplify the expression by subtracting the exponents:

(k^8)/(3k^7) = k^(8-7)/(3) = k/3

Therefore, the simplified form of the expression 4(k^2)^4/12k^7 is k/3.