What is ((-4)^2)/((-4)^7) ?

The solution to ((-4)^2)/((-4)^7) is -1/1024

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((-4)^2)/((-4)^7)

\frac{( - 4 ) ^{2}}{( - 4 ) ^{7}}

- \frac{1}{1024}

Solution steps

\frac{( - 4 ) ^{2}}{( - 4 ) ^{7}}

Solve

(- 4)^{2} : 16

Apply exponent rule:

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

n

is even

(- 4)^{2} = 4^{2} = 16

= 16

Solve

(- 4)^{7} : - 16384

Follow the PEMDAS order of operations

Apply exponent rule:

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

n

is odd

(- 4)^{7} = - 4^{7} = - 16384

= - 16384

= \frac{16}{- 16384}

Simplify

\frac{16}{- 16384} : - \frac{1}{1024}

Apply the fraction rule:

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

= - \frac{16}{16384}

Cancel the common factor:

16

= - \frac{1}{1024}

= - \frac{1}{1024}

- 3 \times 1 - 2

- 3 \times 1 + 6

- 1 (0) + 0

8/12 \times 6/9 \times 5/8

- 3^{2} + 4 (3)