What is (5ax^2)(a^2x^3)(6ax) ?

The solution to (5ax^2)(a^2x^3)(6ax) is 30a^4x^6

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simplify (5ax^2)(a^2x^3)(6ax)

simplify

(5 a x^{2}) (a^{2} x^{3}) (6 a x)

30 a^{4} x^{6}

Solution steps

(5 a x^{2}) (a^{2} x^{3}) (6 a x)

Apply exponent rule:

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

a a^{2} a = a^{1 + 2 + 1}

= 5 x^{2} x^{3} \cdot 6 a^{1 + 2 + 1} x

Add the numbers:

1 + 2 + 1 = 4

= 5 x^{2} x^{3} \cdot 6 a^{4} x

Apply exponent rule:

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

x^{2} x^{3} x = x^{2 + 3 + 1}

= 5 \cdot 6 a^{4} x^{2 + 3 + 1}

Add the numbers:

2 + 3 + 1 = 6

= 5 \cdot 6 a^{4} x^{6}

Multiply the numbers:

5 \cdot 6 = 30

= 30 a^{4} x^{6}

(x - y)^{2} (x + y)^{2}

2 e^{- x}

x^{2} e^{- 2 x}

cos^{2} (x) sin^{2} (x)