What is -(-3)^2\div (-6)^3 ?

The solution to -(-3)^2\div (-6)^3 is 1/24

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-(-3)^2\div (-6)^3

- (- 3)^{2} \div (- 6)^{3}

\frac{1}{24}

Solution steps

- (- 3)^{2} \div (- 6)^{3}

Follow the PEMDAS order of operations

Calculate exponents

(- 3)^{2} : 9

(- 3)^{2}

Apply exponent rule:

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

n

is even

(- 3)^{2} = 3^{2} = 9

= 9

= - 9 \div (- 6)^{3}

Calculate exponents

(- 6)^{3} : - 216

(- 6)^{3}

Apply exponent rule:

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

n

is odd

(- 6)^{3} = - 6^{3} = - 216

= - 216

= - 9 \div (- 216)

Multiply and divide (left to right)

- 9 \div (- 216) : \frac{- 9}{( - 216 )}

- 9 \div (- 216)

Apply rule

- a \div (- b) = a \div b

- 9 \div (- 216) = 9 \div 216 = \frac{- 9}{( - 216 )}

= \frac{- 9}{( - 216 )}

= \frac{- 9}{( - 216 )}

Simplify

\frac{- 9}{( - 216 )} : \frac{1}{24}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{9}{216}

Cancel the common factor:

9

= \frac{1}{24}

- 4 - 2 \times (- 3)

- 2 (- 3) + 2

- 2 (- 3) + 3

((3)^{2} - 2 (- 2) (4))^{2}

(91 + 199) \div 17 - 2 \times (4 + 3) + 1