What is (4x)^{1/2}*(9x)^{1/2} ?

The solution to (4x)^{1/2}*(9x)^{1/2} is 6x

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simplify (4x)^{1/2}*(9x)^{1/2}

simplify

(4 x)^{\frac{1}{2}} \cdot (9 x)^{\frac{1}{2}}

6 x

Solution steps

(4 x)^{\frac{1}{2}} (9 x)^{\frac{1}{2}}

Simplify

(4 x)^{\frac{1}{2}} : 2 x^{\frac{1}{2}}

= 2 x^{\frac{1}{2}} (9 x)^{\frac{1}{2}}

Simplify

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

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

Multiply the numbers:

2 \cdot 3 = 6

= 6 x^{\frac{1}{2}} x^{\frac{1}{2}}

Apply exponent rule:

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

x^{\frac{1}{2}} x^{\frac{1}{2}} = x^{\frac{1}{2} + \frac{1}{2}}

= 6 x^{\frac{1}{2} + \frac{1}{2}}

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

= 6 x^{1}

Apply exponent rule:

a^{1} = a

x^{1} = x

= 6 x

\frac{x}{3} = (4) (3)

\frac{- 162}{- 81}

∣ 2 x - 3 ∣ = ∣ x + 5 ∣

(2 x^{- 2} y^{3})^{4} \cdot 2 x^{19} y^{- 6}

x \cdot (100 - (\frac{1}{( 0.01 ) \cdot ( 1.01 ) ^{240}})) = 300000