What is x^4y^3z^2(x^3y^7z) ?

The solution to x^4y^3z^2(x^3y^7z) is x^7y^{10}z^3

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simplify x^4y^3z^2(x^3y^7z)

simplify

x^{4} y^{3} z^{2} (x^{3} y^{7} z)

x^{7} y^{10} z^{3}

Solution steps

x^{4} y^{3} z^{2} (x^{3} y^{7} z)

Apply exponent rule:

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

x^{4} x^{3} = x^{4 + 3}

= y^{3} z^{2} x^{4 + 3} y^{7} z

Add the numbers:

4 + 3 = 7

= y^{3} z^{2} x^{7} y^{7} z

Apply exponent rule:

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

y^{3} y^{7} = y^{3 + 7}

= z^{2} x^{7} y^{3 + 7} z

Add the numbers:

3 + 7 = 10

= z^{2} x^{7} y^{10} z

Apply exponent rule:

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

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

= x^{7} y^{10} z^{2 + 1}

Add the numbers:

2 + 1 = 3

= x^{7} y^{10} z^{3}

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

5 e^{- t} x sin (t)

e^{- l n ∣ 1 - s i n (t) c o s (t) ∣}

16 a^{6} b^{6}