What is (-8q^3r^4s^2)^2 ?

The solution to (-8q^3r^4s^2)^2 is 64q^6r^8s^4

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simplify (-8q^3r^4s^2)^2

simplify

(- 8 q^{3} r^{4} s^{2})^{2}

64 q^{6} r^{8} s^{4}

Solution steps

(- 8 q^{3} r^{4} s^{2})^{2}

Apply exponent rule:

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

n

is even

(- 8 q^{3} r^{4} s^{2})^{2} = (8 q^{3} r^{4} s^{2})^{2}

= (8 q^{3} r^{4} s^{2})^{2}

Apply exponent rule:

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

(8 q^{3} r^{4} s^{2})^{2} = 8^{2} (q^{3})^{2} (r^{4})^{2} (s^{2})^{2}

= 8^{2} (q^{3})^{2} (r^{4})^{2} (s^{2})^{2}

8^{2} = 64

= 64 (q^{3})^{2} (r^{4})^{2} (s^{2})^{2}

Simplify

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

= 64 q^{6} (r^{4})^{2} (s^{2})^{2}

Simplify

(r^{4})^{2} : r^{8}

= 64 q^{6} r^{8} (s^{2})^{2}

Simplify

(s^{2})^{2} : s^{4}

= 64 q^{6} r^{8} s^{4}

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