What is sqrt(ab)asqrt(ab)sqrt(ab) ?

The solution to sqrt(ab)asqrt(ab)sqrt(ab) is a^{5/2}b^{3/2}

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simplify sqrt(ab)asqrt(ab)sqrt(ab)

simplify

ab a ab ab

a^{\frac{5}{2}} b^{\frac{3}{2}}

Solution steps

ab a ab ab

Apply exponent rule:

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

ab ab ab = (ab)^{\frac{1}{2}} (ab)^{\frac{1}{2}} (ab)^{\frac{1}{2}} = (ab)^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

= a (ab)^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

Combine the fractions

\frac{1}{2} + \frac{1}{2} + \frac{1}{2} : \frac{3}{2}

= a (ab)^{\frac{3}{2}}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(ab)^{\frac{3}{2}} = a^{\frac{3}{2}} b^{\frac{3}{2}}

= a a^{\frac{3}{2}} b^{\frac{3}{2}}

Apply exponent rule:

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

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

= a^{1 + \frac{3}{2}} b^{\frac{3}{2}}

a^{1 + \frac{3}{2}} = a^{\frac{5}{2}}

= a^{\frac{5}{2}} b^{\frac{3}{2}}

20 e^{- 2 \cdot 1}

3.72 \cdot 1 0^{- 5}

15 X 1 0^{- 4} (20.33)

(3 x^{3} y^{2}) (7 y^{3})

2.34 \cdot 1 0^{- 1}

What is sqrt(ab)asqrt(ab)sqrt(ab) ?
The solution to sqrt(ab)asqrt(ab)sqrt(ab) is a^{5/2}b^{3/2}