What is 3^{-1/2}*3x^{9/2}(3x)^{-7/2} ?

The solution to 3^{-1/2}*3x^{9/2}(3x)^{-7/2} is x/(27)

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simplify 3^{-1/2}*3x^{9/2}(3x)^{-7/2}

simplify

3^{- \frac{1}{2}} \cdot 3 x^{\frac{9}{2}} (3 x)^{- \frac{7}{2}}

\frac{x}{27}

Solution steps

3^{- \frac{1}{2}} \cdot 3 x^{\frac{9}{2}} (3 x)^{- \frac{7}{2}}

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

= 3^{\frac{1}{2}} x^{\frac{9}{2}} (3 x)^{- \frac{7}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

= 3^{- \frac{7}{2}} \cdot 3^{\frac{1}{2}} x^{- \frac{7}{2}} x^{\frac{9}{2}}

Apply exponent rule:

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

x^{\frac{9}{2}} x^{- \frac{7}{2}} = x^{\frac{9}{2} - \frac{7}{2}}

= 3^{\frac{1}{2}} \cdot 3^{- \frac{7}{2}} x^{\frac{9}{2} - \frac{7}{2}}

Apply exponent rule:

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

3^{\frac{1}{2}} \cdot 3^{- \frac{7}{2}} = 3^{\frac{1}{2} - \frac{7}{2}}

= 3^{\frac{1}{2} - \frac{7}{2}} x^{\frac{9}{2} - \frac{7}{2}}

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

= 3^{- 3} x^{\frac{9}{2} - \frac{7}{2}}

x^{\frac{9}{2} - \frac{7}{2}} = x

= 3^{- 3} x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

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

Multiply fractions:

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

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

Refine

= \frac{x}{27}

- 20 = x - 17

∣ 7 x - 2 ∣ + 1 \geq 9

2 \leq x + 9 < 4

∣ 2 x - 6 ∣ - ∣ x - 2 ∣ \leq ∣ 2 x - 4 ∣ - ∣ x - 3 ∣

What is 3^{-1/2}*3x^{9/2}(3x)^{-7/2} ?
The solution to 3^{-1/2}*3x^{9/2}(3x)^{-7/2} is x/(27)