What is e^x*2y*4*e^x*y^2 ?

The solution to e^x*2y*4*e^x*y^2 is 8e^{2x}y^3

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simplify e^x2y4e^xy^2

simplify

e^{x} \cdot 2 y \cdot 4 \cdot e^{x} \cdot y^{2}

8 e^{2 x} y^{3}

Solution steps

e^{x} \cdot 2 y \cdot 4 e^{x} y^{2}

Apply exponent rule:

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

e^{x} e^{x} = e^{x + x}

= 2 y \cdot 4 e^{x + x} y^{2}

Add similar elements:

x + x = 2 x

= 2 y \cdot 4 e^{2 x} y^{2}

Apply exponent rule:

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

y y^{2} = y^{1 + 2}

= 2 \cdot 4 e^{2 x} y^{1 + 2}

Add the numbers:

1 + 2 = 3

= 2 \cdot 4 e^{2 x} y^{3}

Multiply the numbers:

2 \cdot 4 = 8

= 8 e^{2 x} y^{3}

40000 \cdot (2.5 \cdot 1 0^{- 3})

1 - e^{3 x}^{2}

12 \cdot 4 (32) (8)

\frac{d}{d x} (2 (x - 2 y^{^{'}} (x)))

a - b \cdot a + b