What is (3x^{9/2}y^{3/5})(9x^{9/2}y) ?

The solution to (3x^{9/2}y^{3/5})(9x^{9/2}y) is 27x^9y^{8/5}

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simplify (3x^{9/2}y^{3/5})(9x^{9/2}y)

simplify

(3 x^{\frac{9}{2}} y^{\frac{3}{5}}) (9 x^{\frac{9}{2}} y)

27 x^{9} y^{\frac{8}{5}}

Solution steps

(3 x^{\frac{9}{2}} y^{\frac{3}{5}}) (9 x^{\frac{9}{2}} y)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{\frac{9}{2}} x^{\frac{9}{2}} = x^{\frac{9}{2} + \frac{9}{2}}

= 3 y^{\frac{3}{5}} \cdot 9 x^{\frac{9}{2} + \frac{9}{2}} y

Combine the fractions

\frac{9}{2} + \frac{9}{2} : 9

= 3 \cdot 9 x^{9} y y^{\frac{3}{5}}

Multiply the numbers:

3 \cdot 9 = 27

= 27 x^{9} y y^{\frac{3}{5}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

y^{\frac{3}{5}} y = y^{\frac{3}{5} + 1}

= 27 x^{9} y^{\frac{3}{5} + 1}

y^{\frac{3}{5} + 1} = y^{\frac{8}{5}}

= 27 x^{9} y^{\frac{8}{5}}

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What is (3x^{9/2}y^{3/5})(9x^{9/2}y) ?
The solution to (3x^{9/2}y^{3/5})(9x^{9/2}y) is 27x^9y^{8/5}