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

The solution to (4x)^{-1/2}*(9x)^{1/2} is 3/2

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

simplify

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

\frac{3}{2}

Decimal Notation

1.5

Solution steps

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

Simplify

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

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

Simplify

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

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

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Multiply the numbers:

1 \cdot 3 = 3

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

Cancel the common factor:

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

= \frac{3}{2}

2 x^{2} + 3 x - 14

x^{2} - 3 x - 2.2 = 0

7 x + 8 > 4 x + 4

\frac{a}{3} > 12

x^{2} - 7 x = 0