simplify (-3a^2)^3

Solution

simplify

(- 3 a^{2})^{3}

- 27 a^{6}

Solution steps

(- 3 a^{2})^{3}

Apply exponent rule:

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

n

is odd

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

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

Apply exponent rule:

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

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

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

3^{3} = 27

= - 27 (a^{2})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(a^{2})^{3} = a^{2 \cdot 3}

= - 27 a^{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= - 27 a^{6}

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