What is b^4(3ab^3)(2a^2b^5) ?

The solution to b^4(3ab^3)(2a^2b^5) is 6b^{12}a^3

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simplify b^4(3ab^3)(2a^2b^5)

simplify

b^{4} (3 a b^{3}) (2 a^{2} b^{5})

6 b^{12} a^{3}

Solution steps

b^{4} (3 a b^{3}) (2 a^{2} b^{5})

Apply exponent rule:

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

b^{4} b^{3} b^{5} = b^{4 + 3 + 5}

= 3 a \cdot 2 a^{2} b^{4 + 3 + 5}

Add the numbers:

4 + 3 + 5 = 12

= 3 a \cdot 2 a^{2} b^{12}

Apply exponent rule:

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

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

= 3 \cdot 2 a^{1 + 2} b^{12}

Add the numbers:

1 + 2 = 3

= 3 \cdot 2 a^{3} b^{12}

Multiply the numbers:

3 \cdot 2 = 6

= 6 b^{12} a^{3}

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