What is (-a*b^5*c^1*1)^6 ?

The solution to (-a*b^5*c^1*1)^6 is a^6b^{30}c^6

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simplify (-ab^5c^1*1)^6

simplify

(- a \cdot b^{5} \cdot c^{1} \cdot 1)^{6}

a^{6} b^{30} c^{6}

Solution steps

(- a b^{5} c^{1} \cdot 1)^{6}

Apply exponent rule:

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

n

is even

(- a b^{5} c^{1} \cdot 1)^{6} = (a b^{5} c^{1} \cdot 1)^{6}

= (a b^{5} c^{1} \cdot 1)^{6}

Apply exponent rule:

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

(a b^{5} c^{1} \cdot 1)^{6} = a^{6} (b^{5})^{6} (c^{1})^{6} \cdot 1^{6}

= a^{6} (b^{5})^{6} (c^{1})^{6} \cdot 1^{6}

Simplify

(b^{5})^{6} : b^{30}

= a^{6} b^{30} (c^{1})^{6} \cdot 1^{6}

Simplify

(c^{1})^{6} : c^{6}

= a^{6} b^{30} c^{6} \cdot 1^{6}

1^{6} = 1

= a^{6} b^{30} c^{6} \cdot 1

Multiply:

c^{6} \cdot 1 = c^{6}

= a^{6} b^{30} c^{6}

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