What is expand 4(1-2/16 x)^{1/2} ?

The solution to expand 4(1-2/16 x)^{1/2} is 2^{1/2}(-x+8)^{1/2}

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expand 4(1-2/16 x)^{1/2}

expand

4 (1 - \frac{2}{16} x)^{\frac{1}{2}}

2^{\frac{1}{2}} (- x + 8)^{\frac{1}{2}}

Solution steps

4 (1 - \frac{2}{16} x)^{\frac{1}{2}}

(1 - \frac{2}{16} x)^{\frac{1}{2}} = \frac{( 8 - x ) ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}

= 4 \cdot \frac{( - x + 8 ) ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}

Multiply fractions:

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

= \frac{( 8 - x ) ^{\frac{1}{2}} \cdot 4}{2 \cdot 2 ^{\frac{1}{2}}}

Divide the numbers:

\frac{4}{2} = 2

= \frac{2 ( - x + 8 ) ^{\frac{1}{2}}}{2 ^{\frac{1}{2}}}

Apply exponent rule:

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

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

= 2^{- \frac{1}{2} + 1} (- x + 8)^{\frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 2^{\frac{1}{2}} (- x + 8)^{\frac{1}{2}}

(x - (3 i + 1)) (x - (1 - 3 i))

sin (4 (t - w))

s \cdot (1 + \frac{s}{3}) (1 + \frac{s}{20})

\frac{1}{2} (lo g_{5} (x - 8) - lo g_{10} (5 x))

sin (2 t) U (t - 2 π)

What is expand 4(1-2/16 x)^{1/2} ?
The solution to expand 4(1-2/16 x)^{1/2} is 2^{1/2}(-x+8)^{1/2}