What is (1(-10)^{-7})^{512} ?

The solution to (1(-10)^{-7})^{512} is 1/(10^{3584)}

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simplify (1(-10)^{-7})^{512}

simplify

(1 (- 10)^{- 7})^{512}

\frac{1}{1 0 ^{3584}}

Solution steps

(1 \cdot (- 10)^{- 7})^{512}

Apply exponent rule:

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

(1 \cdot (- 10)^{- 7})^{512} = 1^{512} ((- 10)^{- 7})^{512}

= 1^{512} ((- 10)^{- 7})^{512}

1^{512} = 1

= 1 \cdot ((- 10)^{- 7})^{512}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

((- 10)^{- 7})^{512} = (- 10)^{- 7 \cdot 512}

= 1 \cdot (- 10)^{- 7 \cdot 512}

Multiply the numbers:

7 \cdot 512 = 3584

= 1 \cdot (- 10)^{- 3584}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(- 10)^{- 3584} = \frac{1}{( - 10 ) ^{3584}}

= 1 \cdot \frac{1}{( - 10 ) ^{3584}}

Apply exponent rule:

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

n

is even

(- 10)^{3584} = 1 0^{3584}

= 1 \cdot \frac{1}{1 0 ^{3584}}

Multiply:

1 \cdot \frac{1}{1 0 ^{3584}} = \frac{1}{1 0 ^{3584}}

= \frac{1}{1 0 ^{3584}}

(n - 3) e^{- n}

- e (e^{- x})

2^{x^{2}} 2 x ln (2)

What is (1(-10)^{-7})^{512} ?
The solution to (1(-10)^{-7})^{512} is 1/(10^{3584)}