What is e^{-(4x^2+4y^2+4z^2)^{3/2}} ?

The solution to e^{-(4x^2+4y^2+4z^2)^{3/2}} is 1/(e^{8(x^2+y^2+z^2)^{3/2)}}

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simplify e^{-(4x^2+4y^2+4z^2)^{3/2}}

simplify

e^{- (4 x^{2} + 4 y^{2} + 4 z^{2})^{\frac{3}{2}}}

\frac{1}{e ^{8 (x^{2} + y^{2} + z^{2})^{\frac{3}{2}}}}

Solution steps

e^{- (4 x^{2} + 4 y^{2} + 4 z^{2})^{\frac{3}{2}}}

Apply exponent rule:

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

= \frac{1}{e ^{(4 x^{2} + 4 y^{2} + 4 z^{2})^{\frac{3}{2}}}}

e^{(4 x^{2} + 4 y^{2} + 4 z^{2})^{\frac{3}{2}}} = e^{8 (x^{2} + y^{2} + z^{2})^{\frac{3}{2}}}

= \frac{1}{e ^{8 (x^{2} + y^{2} + z^{2})^{\frac{3}{2}}}}

- 3^{2}

1 + x 1 - x

(\frac{2}{5})^{- 3} l e f t (\frac{3}{7})^{- 3}

(23) (35)

(2 x^{3}) l e f t (5 x^{3})

What is e^{-(4x^2+4y^2+4z^2)^{3/2}} ?
The solution to e^{-(4x^2+4y^2+4z^2)^{3/2}} is 1/(e^{8(x^2+y^2+z^2)^{3/2)}}