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# algebra

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Work out the the value of k.

Sep 14, 2020

#1
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If we multiply cbrt(a) on both the denominator and numerator, we get (a*sqrt(a)*cbrt(a))/a. The a's cancel out and we are left with sqrt(a)*cbrt(a) = a^k. sqrt(a) can also be written as a^(1/2) and cbrt(a) can be written as a^(1/3). Because they are multiplying each other, we add the exponent to get k = 5/6

Sep 14, 2020
#3
+26
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I think asinus has a much cleaner explanation... check out theirs

Awesomeguy  Sep 14, 2020
#2
+10838
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Work out the the value of k.

Hello Guest!

$$\frac{a\sqrt{a}}{\sqrt[3]{a^2}}=a^k$$

$$a^{1+\frac{1}{2}-\frac{2}{3}}=a^k$$

$$k=1+\frac{1}{2}-\frac{2}{3}=\frac{6+3-4}{6}$$

$$k=\frac{5}{6}$$

!

Sep 14, 2020