What is (1.6x10^{-19})(8x10^6)(2.5)(sin(60)) ?

The solution to (1.6x10^{-19})(8x10^6)(2.5)(sin(60)) is (sqrt(3)x^2)/(5^{13)*512}

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simplify (1.6x10^{-19})(8x10^6)(2.5)(sin(60))

simplify

(1.6 x 1 0^{- 19}) (8 x 1 0^{6}) (2.5) (sin (6 0^{\circ}))

\frac{3 x ^{2}}{5 ^{13} \cdot 512}

Solution steps

(1.6 x \cdot 1 0^{- 19}) (8 x \cdot 1 0^{6}) (2.5) (sin (6 0^{\circ}))

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

xx = x^{1 + 1}

= 1.6 \cdot 1 0^{- 19} \cdot 8 x^{1 + 1} \cdot 1 0^{6} \cdot 2.5 sin (6 0^{\circ})

Add the numbers:

1 + 1 = 2

= 1.6 \cdot 1 0^{- 19} \cdot 8 x^{2} \cdot 1 0^{6} \cdot 2.5 sin (6 0^{\circ})

Factor integer

10 = 2 \cdot 5

= 1.6 (2 \cdot 5)^{- 19} \cdot 8 x^{2} \cdot 1 0^{6} \cdot 2.5 sin (6 0^{\circ})

Apply exponent rule:

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

(2 \cdot 5)^{- 19} = 2^{- 19} \cdot 5^{- 19}

= 1.6 \cdot 2^{- 19} \cdot 5^{- 19} \cdot 8 x^{2} \cdot 1 0^{6} \cdot 2.5 sin (6 0^{\circ})

Factor integer

8 = 2^{3}

= 1.6 \cdot 2^{- 19} \cdot 5^{- 19} \cdot 2^{3} x^{2} \cdot 1 0^{6} \cdot 2.5 sin (6 0^{\circ})

Factor integer

10 = 2 \cdot 5

= 1.6 \cdot 2^{- 19} \cdot 5^{- 19} \cdot 2^{3} x^{2} (2 \cdot 5)^{6} \cdot 2.5 sin (6 0^{\circ})

Apply exponent rule:

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

(2 \cdot 5)^{6} = 2^{6} \cdot 5^{6}

= 1.6 \cdot 2^{- 19} \cdot 5^{- 19} \cdot 2^{3} x^{2} \cdot 2^{6} \cdot 5^{6} \cdot 2.5 sin (6 0^{\circ})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{- 19} \cdot 2^{3} \cdot 2^{6} = 2^{- 19 + 3 + 6}

= 1.6 \cdot 5^{- 19} x^{2} \cdot 2^{- 19 + 3 + 6} \cdot 5^{6} \cdot 2.5 sin (6 0^{\circ})

Add/Subtract the numbers:

- 19 + 3 + 6 = - 10

= 1.6 \cdot 5^{- 19} x^{2} \cdot 2^{- 10} \cdot 5^{6} \cdot 2.5 sin (6 0^{\circ})

Apply exponent rule:

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

5^{- 19} = \frac{1}{5 ^{19}}

= 2^{- 10} \cdot 5^{6} \cdot 1.6 \cdot 2.5 \cdot \frac{1}{5 ^{19}} sin (6 0^{\circ}) x^{2}

Apply exponent rule:

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

2^{- 10} = \frac{1}{2 ^{10}}

= 5^{6} \cdot 1.6 \cdot 2.5 \cdot \frac{1}{5 ^{19}} \cdot \frac{1}{2 ^{10}} sin (6 0^{\circ}) x^{2}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= 1.6 \cdot 2.5 sin (6 0^{\circ}) \frac{5 ^{6} \cdot 1 \cdot 1 \cdot x ^{2}}{5 ^{19} \cdot 2 ^{10}}

Simplify

\frac{1 \cdot 1 \cdot 5 ^{6} x ^{2}}{5 ^{19} \cdot 2 ^{10}} : \frac{x ^{2}}{5 ^{13} \cdot 1024}

= 1.6 \cdot 2.5 sin (6 0^{\circ}) \frac{x ^{2}}{5 ^{13} \cdot 1024}

Simplify

sin (6 0^{\circ}) : \frac{3}{2}

= 1.6 \cdot 2.5 \cdot \frac{3}{2} \cdot \frac{x ^{2}}{5 ^{13} \cdot 1024}

Simplify

= \frac{3 x ^{2}}{5 ^{13} \cdot 512}

(1.67 \cdot 1 0^{- 8}) \cdot (250)

(e^{2 α}) \cdot e^{2 α}

81 (1 0^{- 6}) π

f (x) = - 3 x

\frac{e ^{x + 2}}{e ^{x}}

What is (1.6x10^{-19})(8x10^6)(2.5)(sin(60)) ?
The solution to (1.6x10^{-19})(8x10^6)(2.5)(sin(60)) is (sqrt(3)x^2)/(5^{13)*512}