(n^(6)k^(14))^(5) Which of the following is equivalent to the given expression? Choose 1 answer: (A) (n^(2)k^(5))^(3) (B) (n^(3))^(10)(k^(2))^(7) (C) (n^(15)k^(35))^(2) (D) (n^(5))^(5)(k^(10))^(7)

Question

(n^(6)k^(14))^(5) Which of the following is equivalent to the given expression? Choose 1 answer: (A)  (n^(2)k^(5))^(3) (B)  (n^(3))^(10)(k^(2))^(7) (C)  (n^(15)k^(35))^(2) (D)  (n^(5))^(5)(k^(10))^(7)

Bytelearn · Accepted Answer

Apply power of power rule: Apply the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). We will apply this rule to both n^6 and k^14 raised to the 5th power.Calculate new exponents: Calculate the new exponents for n and k. For n^6 raised to the 5th power, the new exponent is 6*5 = 30. For k^14 raised to the 5th power, the new exponent is 14*5 = 70. So, (n^(6)k^(14))^(5) = n^(30)k^(70).Compare with given options: Compare the result with the given options. We have n^(30)k^(70). Now we need to check which option is equivalent to this expression.  Option (A) (n^(2)k^(5))^(3) would give us n^(2*3)k^(5*3) = n^(6)k^(15), which is not equivalent.  Option (B) (n^(3))^(10)(k^(2))^(7) would give us n^(3*10)k^(2*7) = n^(30)k^(14), which is also not equivalent.  Option (C) (n^(15)k^(35))^(2) would give us n^(15*2)k^(35*2) = n^(30)k^(70), which is equivalent to our expression.  Option (D) (n^(5))^(5)(k^(10))^(7) would give us n^(5*5)k^(10*7) = n^(25)k^(70), which is not equivalent.  Therefore, the correct answer is Option (C).

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