What is x^5(3x^2y)(4x^3y^2) ?

The solution to x^5(3x^2y)(4x^3y^2) is 12x^{10}y^3

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simplify x^5(3x^2y)(4x^3y^2)

simplify

x^{5} (3 x^{2} y) (4 x^{3} y^{2})

12 x^{10} y^{3}

Solution steps

x^{5} (3 x^{2} y) (4 x^{3} y^{2})

Apply exponent rule:

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

x^{5} x^{2} x^{3} = x^{5 + 2 + 3}

= 3 y \cdot 4 x^{5 + 2 + 3} y^{2}

Add the numbers:

5 + 2 + 3 = 10

= 3 y \cdot 4 x^{10} y^{2}

Apply exponent rule:

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

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

= 3 \cdot 4 x^{10} y^{1 + 2}

Add the numbers:

1 + 2 = 3

= 3 \cdot 4 x^{10} y^{3}

Multiply the numbers:

3 \cdot 4 = 12

= 12 x^{10} y^{3}

e^{2} \times e^{5}

(x + 4) \cdot e^{- x}

((x^{2})^{- 3})^{\frac{1}{4}}

e^{- x} \cdot \frac{1}{2} e^{\frac{x}{2}}

- e^{- x} \cdot e^{4 x}

What is x^5(3x^2y)(4x^3y^2) ?
The solution to x^5(3x^2y)(4x^3y^2) is 12x^{10}y^3