What is simplify-2re^{r^2}sin(θ)*2r*(-2)sin(θ)*e^{r^2} ?

The solution to simplify-2re^{r^2}sin(θ)*2r*(-2)sin(θ)*e^{r^2} is 8e^{2r^2}r^2sin^2(θ)

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simplify-2re^{r^2}sin(θ)2r(-2)sin(θ)*e^{r^2}

simplify

- 2 r e^{r^{2}} sin (θ) \cdot 2 r \cdot (- 2) sin (θ) \cdot e^{r^{2}}

8 e^{2 r^{2}} r^{2} sin^{2} (θ)

Solution steps

- 2 r e^{r^{2}} sin (θ) \cdot 2 r (- 2) sin (θ) e^{r^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2 = 2^{1 + 1}

= - r e^{r^{2}} sin (θ) \cdot 2^{1 + 1} r (- 2) sin (θ) e^{r^{2}}

Add the numbers:

1 + 1 = 2

= - r e^{r^{2}} sin (θ) \cdot 2^{2} r (- 2) sin (θ) e^{r^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sin (θ) sin (θ) = sin^{1 + 1} (θ)

= - r e^{r^{2}} \cdot 2^{2} r (- 2) sin^{1 + 1} (θ) e^{r^{2}}

Add the numbers:

1 + 1 = 2

= - r e^{r^{2}} \cdot 2^{2} r (- 2) sin^{2} (θ) e^{r^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{r^{2}} e^{r^{2}} = e^{r^{2} + r^{2}}

= - r \cdot 2^{2} r (- 2) sin^{2} (θ) e^{r^{2} + r^{2}}

Add similar elements:

r^{2} + r^{2} = 2 r^{2}

= - r \cdot 2^{2} r (- 2) sin^{2} (θ) e^{2 r^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

rr = r^{1 + 1}

= - 2^{2} r^{1 + 1} (- 2) sin^{2} (θ) e^{2 r^{2}}

Add the numbers:

1 + 1 = 2

= - 2^{2} r^{2} (- 2) sin^{2} (θ) e^{2 r^{2}}

Apply rule

- (- a) = a

= 2^{2} r^{2} \cdot 2 sin^{2} (θ) e^{2 r^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{2} \cdot 2 = 2^{2 + 1}

= r^{2} \cdot 2^{2 + 1} sin^{2} (θ) e^{2 r^{2}}

Refine

= 8 e^{2 r^{2}} r^{2} sin^{2} (θ)

4 (m^{3} n)^{5}

(2.66 \cdot 1 0^{- 23}) (6.02214 \cdot 1 0^{23})

in t er sec (c) i o n es (x - 1)^{4}

(x - 1)^{2} e^{- x}

What is simplify-2re^{r^2}sin(θ)*2r*(-2)sin(θ)*e^{r^2} ?
The solution to simplify-2re^{r^2}sin(θ)*2r*(-2)sin(θ)*e^{r^2} is 8e^{2r^2}r^2sin^2(θ)