What is (x^4y^2z)(xy^3z^2) ?

The solution to (x^4y^2z)(xy^3z^2) is x^5y^5z^3

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simplify (x^4y^2z)(xy^3z^2)

simplify

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

x^{5} y^{5} z^{3}

Solution steps

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

Apply exponent rule:

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

x^{4} x = x^{4 + 1}

= y^{2} z x^{4 + 1} y^{3} z^{2}

Add the numbers:

4 + 1 = 5

= y^{2} z x^{5} y^{3} z^{2}

Apply exponent rule:

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

y^{2} y^{3} = y^{2 + 3}

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

Add the numbers:

2 + 3 = 5

= z x^{5} y^{5} z^{2}

Apply exponent rule:

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

z z^{2} = z^{1 + 2}

= x^{5} y^{5} z^{1 + 2}

Add the numbers:

1 + 2 = 3

= x^{5} y^{5} z^{3}

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

3583 e^{(- e^{(- 0.02 (t - 66))})}

⎩ ⎨ ⎧ [(- \frac{1}{7})^{2}]^{- 1} ⎭ ⎬ ⎫^{- 1}

800000 \cdot e^{- 0.14 \cdot 3}

x^{n} y^{n}