What is $- 5 a b^{3} \cdot 7 a^{2} b^{3}$ $-5ab^3 * 7a^2b^3$ ?

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What is $- 5 a b^{3} \cdot 7 a^{2} b^{3}$ $-5ab^3 * 7a^2b^3$ ?

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Answer 1 · 2017-01-31T13:35:27

$- 35 a^{3} b^{6}$ $-35a^3b^6$

Explanation:

First, rearrange to group like terms:

$(- 5 \cdot 7) (a \cdot a^{2}) (b^{3} \cdot b^{3}) = - 35 (a \cdot a^{2}) (b^{3} \cdot b^{3})$ $(-5*7)(a*a^2)(b^3*b^3) = -35(a*a^2)(b^3*b^3)$

Next, use these rules for exponents to multiply the variable terms:

$a = a^{1}$ $a = a^color(red)(1)$

$x^{a} \times x^{b} = x^{a + b}$ $x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))$

$- 35 (a^{1} \cdot a^{2}) (b^{3} \cdot b^{3}) = - 35 a^{1 + 2} b^{3 + 3} = - 35 a^{3} b^{6}$ $-35(a^color(red)(1)*a^2)(b^3*b^3) = -35a^(1+2)b^(3+3) = -35a^3b^6$

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What is $- 5 a b^{3} \cdot 7 a^{2} b^{3}$ $-5ab^3 * 7a^2b^3$ ?

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