Answer:
The simplified form of given expression\(\frac{15xy}{5x^{\frac{1}{2}}y^2}\) is \(\frac{3x^{\frac{1}{2}}}{y}\)
Step-by-step explanation:
Given: Expression \(\frac{15xy}{5x^{\frac{1}{2}}y^2}\)
We have to write the given expression in simplified form,
Consider the given expression \(\frac{15xy}{5x^{\frac{1}{2}}y^2}\)
Divide the numbers \(\frac{15}{5}=3\)
we get,
\(=\frac{3xy}{y^2x^{\frac{1}{2}}}\)
Apply exponent rule , \(\frac{x^a}{x^b}\:=\:x^{a-b}\)
\(\frac{x}{x^{\frac{1}{2}}}=x^{1-\frac{1}{2}}=x^{\frac{1}{2}}\)
we get,
\(=\frac{3yx^{\frac{1}{2}}}{y^2}\)
Cancel y term, we have,
\(=\frac{3x^{\frac{1}{2}}}{y}\)
Thus, The simplified form of given expression\(\frac{15xy}{5x^{\frac{1}{2}}y^2}\) is \(\frac{3x^{\frac{1}{2}}}{y}\)
