What is 9^{3/4}*3^{-1/2} ?

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

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simplify 9^{3/4}*3^{-1/2}

simplify

9^{\frac{3}{4}} \cdot 3^{- \frac{1}{2}}

3

Solution steps

9^{\frac{3}{4}} \cdot 3^{- \frac{1}{2}}

9^{\frac{3}{4}} = 3 \cdot 3^{\frac{1}{2}}

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

Apply exponent rule:

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

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

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

Convert

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

to fraction

: \frac{3 ^{\frac{1}{2}}}{1}

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

Cross-cancel common factor:

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

= 3 \cdot 1

Multiply the numbers:

3 \cdot 1 = 3

= 3

x + \frac{1}{x - 2} + \frac{2}{( x + 6 ) ( x - 2 )} - 2 \geq x - \frac{3}{x + 6} - 2

(x - 3)^{2} (x + 6) > 0

(9^{\frac{5}{3}})^{\frac{3}{10}}

11 h - (2 h - 1) = 118

x^{2} - 10 x + 25 = 3