What is 5(-a^3b^2c)^3 ?

The solution to 5(-a^3b^2c)^3 is -5a^9b^6c^3

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simplify 5(-a^3b^2c)^3

simplify

5 (- a^{3} b^{2} c)^{3}

- 5 a^{9} b^{6} c^{3}

Solution steps

5 (- a^{3} b^{2} c)^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- a^{3} b^{2} c)^{3} = - (a^{3} b^{2} c)^{3}

= 5 (- (a^{3} b^{2} c)^{3})

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(a^{3} b^{2} c)^{3} = (a^{3})^{3} (b^{2})^{3} c^{3}

= 5 (- (a^{3})^{3} (b^{2})^{3} c^{3})

Simplify

(a^{3})^{3} : a^{9}

= 5 (- a^{9} (b^{2})^{3} c^{3})

Simplify

(b^{2})^{3} : b^{6}

= 5 (- a^{9} b^{6} c^{3})

Apply rule:

a (- b) = - ab

5 (- a^{9} b^{6} c^{3}) = - 5 a^{9} b^{6} c^{3}

= - 5 a^{9} b^{6} c^{3}

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