Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which exponential expression is equivalent to 
root(6)(k^(5)) ?
Choose 1 answer:
(A) 
(k^(6))/(k^(5))
(B) 
(k^(5))/(k^(6))
(c) 
k^((5)/(6))
(D) 
k^((6)/(5))

Which exponential expression is equivalent to k56 \sqrt[6]{k^{5}} ?\newlineChoose 11 answer:\newline(A) k6k5 \frac{k^{6}}{k^{5}} \newline(B) k5k6 \frac{k^{5}}{k^{6}} \newline(C) k56 k^{\frac{5}{6}} \newline(D) k65 k^{\frac{6}{5}}

Full solution

Q. Which exponential expression is equivalent to k56 \sqrt[6]{k^{5}} ?\newlineChoose 11 answer:\newline(A) k6k5 \frac{k^{6}}{k^{5}} \newline(B) k5k6 \frac{k^{5}}{k^{6}} \newline(C) k56 k^{\frac{5}{6}} \newline(D) k65 k^{\frac{6}{5}}
  1. Expressing the root as an exponent: To find an equivalent exponential expression for the sixth root of kk to the power of 55, we need to express the root as an exponent.\newlineThe sixth root of a number is the same as raising that number to the power of 1/61/6.\newlineSo, the sixth root of k5k^5 is k(51/6)k^{(5 * 1/6)}.
  2. Finding the equivalent expression: Now, we multiply the exponents to find the equivalent expression. 5×16=565 \times \frac{1}{6} = \frac{5}{6} Therefore, the sixth root of k5k^5 is k56k^{\frac{5}{6}}.

More problems from Identify equivalent linear expressions