What is [((27x^7*y^3))/((3x^3*y))]^{1/2} ?

The solution to [((27x^7*y^3))/((3x^3*y))]^{1/2} is 3x^2y

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simplify [((27x^7y^3))/((3x^3y))]^{1/2}

simplify

[\frac{( 27 x ^{7} \cdot y ^{3} )}{( 3 x ^{3} \cdot y )}]^{\frac{1}{2}}

3 x^{2} y

Solution steps

(\frac{27 x ^{7} y ^{3}}{3 x ^{3} y})^{\frac{1}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 27 x ^{7} y ^{3} ) ^{\frac{1}{2}}}{( 3 x ^{3} y ) ^{\frac{1}{2}}}

Simplify

(27 x^{7} y^{3})^{\frac{1}{2}} : 3 \cdot 3^{\frac{1}{2}} x^{\frac{7}{2}} y^{\frac{3}{2}}

= \frac{3 \cdot 3 ^{\frac{1}{2}} x ^{\frac{7}{2}} y ^{\frac{3}{2}}}{( 3 x ^{3} y ) ^{\frac{1}{2}}}

Simplify

(3 x^{3} y)^{\frac{1}{2}} : 3^{\frac{1}{2}} x^{\frac{3}{2}} y^{\frac{1}{2}}

= \frac{3 \cdot 3 ^{\frac{1}{2}} x ^{\frac{7}{2}} y ^{\frac{3}{2}}}{3 ^{\frac{1}{2}} x ^{\frac{3}{2}} y ^{\frac{1}{2}}}

3 \cdot 3^{\frac{1}{2}} x^{\frac{7}{2}} y^{\frac{3}{2}} = 3^{1 + \frac{1}{2}} x^{\frac{7}{2}} y^{\frac{3}{2}}

= \frac{3 ^{\frac{1}{2} + 1} x ^{\frac{7}{2}} y ^{\frac{3}{2}}}{3 ^{\frac{1}{2}} x ^{\frac{3}{2}} y ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{\frac{1}{2} + 1}}{3 ^{\frac{1}{2}}} = 3^{1 + \frac{1}{2} - \frac{1}{2}}

= \frac{3 ^{\frac{1}{2} - \frac{1}{2} + 1} x ^{\frac{7}{2}} y ^{\frac{3}{2}}}{x ^{\frac{3}{2}} y ^{\frac{1}{2}}}

Subtract the numbers:

1 + \frac{1}{2} - \frac{1}{2} = 1

= \frac{3 x ^{\frac{7}{2}} y ^{\frac{3}{2}}}{x ^{\frac{3}{2}} y ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{x ^{\frac{7}{2}}}{x ^{\frac{3}{2}}} = x^{\frac{7}{2} - \frac{3}{2}}

= \frac{3 y ^{\frac{3}{2}} x ^{\frac{7}{2} - \frac{3}{2}}}{y ^{\frac{1}{2}}}

Subtract the numbers:

\frac{7}{2} - \frac{3}{2} = 2

= \frac{3 x ^{2} y ^{\frac{3}{2}}}{y ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{y ^{\frac{3}{2}}}{y ^{\frac{1}{2}}} = y^{\frac{3}{2} - \frac{1}{2}}

= 3 x^{2} y^{\frac{3}{2} - \frac{1}{2}}

Subtract the numbers:

\frac{3}{2} - \frac{1}{2} = 1

= 3 x^{2} y

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What is [((27x^7*y^3))/((3x^3*y))]^{1/2} ?
The solution to [((27x^7*y^3))/((3x^3*y))]^{1/2} is 3x^2y