algebra

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

Work out the the value of k.

Hello Guest!

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

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

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

\(k=\frac{5}{6}\)

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