What is 1/3 (sqrt(7)^2+1)^{-2/3}*4 ?

The solution to 1/3 (sqrt(7)^2+1)^{-2/3}*4 is 1/3

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simplify 1/3 (sqrt(7)^2+1)^{-2/3}*4

simplify

\frac{1}{3} (7^{2} + 1)^{- \frac{2}{3}} \cdot 4

\frac{1}{3}

Solution steps

\frac{1}{3} ((7)^{2} + 1)^{- \frac{2}{3}} \cdot 4

Apply exponent rule:

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

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

= \frac{1}{3} \cdot \frac{1}{( ( 7 ) ^{2} + 1 ) ^{\frac{2}{3}}} \cdot 4

((7)^{2} + 1)^{\frac{2}{3}} = 4

= \frac{1}{3} \cdot \frac{1}{4} \cdot 4

\frac{1}{3} \cdot \frac{1}{4} \cdot 4 = \frac{1}{3}

= \frac{1}{3}

(e^{- 7})^{\frac{6}{7}}

- (2)^{3} (4 - 22)

e^{2 x} \cdot e^{- 3 x}

What is 1/3 (sqrt(7)^2+1)^{-2/3}*4 ?
The solution to 1/3 (sqrt(7)^2+1)^{-2/3}*4 is 1/3