What is ((1.5*10^4+50*10^2))/(7.5)*10^{-12} ?

The solution to ((1.5*10^4+50*10^2))/(7.5)*10^{-12} is 2.66667E-9

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simplify ((1.510^4+5010^2))/(7.5)*10^{-12}

simplify

\frac{( 1.5 \cdot 1 0 ^{4} + 50 \cdot 1 0 ^{2} )}{7.5} \cdot 1 0^{- 12}

2.66667 E - 9

Solution steps

\frac{( 1.5 \cdot 1 0 ^{4} + 50 \cdot 1 0 ^{2} )}{7.5} \cdot 1 0^{- 12}

Apply exponent rule:

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

= \frac{1}{1 0 ^{12}} \cdot \frac{1 0 ^{4} \cdot 1.5 + 1 0 ^{2} \cdot 50}{7.5}

1.5 \cdot 1 0^{4} + 50 \cdot 1 0^{2} = 20000

= \frac{20000}{7.5} \cdot \frac{1}{1 0 ^{12}}

Multiply fractions:

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

= \frac{20000 \cdot 1}{7.5 \cdot 1 0 ^{12}}

Multiply the numbers:

20000 \cdot 1 = 20000

= \frac{20000}{1 0 ^{12} \cdot 7.5}

Factor

20000 : 2^{5} \cdot 5^{4}

Factor

1 0^{12} : 2^{12} \cdot 5^{12}

= \frac{2 ^{5} \cdot 5 ^{4}}{2 ^{12} \cdot 5 ^{12} \cdot 7.5}

Cancel

\frac{2 ^{5} \cdot 5 ^{4}}{7.5 \cdot 2 ^{12} \cdot 5 ^{12}} : \frac{1}{5 ^{8} \cdot 2 ^{7} \cdot 7.5}

= \frac{1}{5 ^{8} \cdot 2 ^{7} \cdot 7.5}

5^{8} \cdot 2^{7} \cdot 7.5 = 375000000

= \frac{1}{375000000}

Convert element to a decimal form

\frac{1}{375000000} = 2.66667 E - 9

= 2.66667 E - 9

e^{- t} t cos (2 t)

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What is ((1.5*10^4+50*10^2))/(7.5)*10^{-12} ?
The solution to ((1.5*10^4+50*10^2))/(7.5)*10^{-12} is 2.66667E-9