What is expand 1/3 (1-10/9 x)^{-1/2} ?

The solution to expand 1/3 (1-10/9 x)^{-1/2} is 1/((-10x+9)^{1/2)}

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expand 1/3 (1-10/9 x)^{-1/2}

expand

\frac{1}{3} (1 - \frac{10}{9} x)^{- \frac{1}{2}}

\frac{1}{( - 10 x + 9 ) ^{\frac{1}{2}}}

Solution steps

\frac{1}{3} (1 - \frac{10}{9} x)^{- \frac{1}{2}}

Apply exponent rule:

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

= \frac{1}{3} \cdot \frac{1}{( - \frac{10}{9} x + 1 ) ^{\frac{1}{2}}}

\frac{1}{( 1 - \frac{10}{9} x ) ^{\frac{1}{2}}} = \frac{3}{( 9 - 10 x ) ^{\frac{1}{2}}}

= \frac{1}{3} \cdot \frac{3}{( - 10 x + 9 ) ^{\frac{1}{2}}}

Multiply fractions:

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

= \frac{1 \cdot 3}{3 ( 9 - 10 x ) ^{\frac{1}{2}}}

Cancel the common factor:

3

= \frac{1}{( 9 - 10 x ) ^{\frac{1}{2}}}

7 (11) e^{- \frac{11}{11}}

2 \frac{x}{x + 1} \cdot (x + 1)^{2}

2 (2.31 \cdot 1 0^{- 19} [\frac{( + 1 ) ( - 1 )}{0.8}])

4^{n} (- \frac{1}{4})^{n}

What is expand 1/3 (1-10/9 x)^{-1/2} ?
The solution to expand 1/3 (1-10/9 x)^{-1/2} is 1/((-10x+9)^{1/2)}