What is 6(5)(7.5)^4e^{-(5(7.5))/4}[1-1/4 (7.5)] ?

The solution to 6(5)(7.5)^4e^{-(5(7.5))/4}[1-1/4 (7.5)] is -7.04471…

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simplify 6(5)(7.5)^4e^{-(5(7.5))/4}[1-1/4 (7.5)]

simplify

6 (5) (7.5)^{4} e^{- \frac{5 ( 7.5 )}{4}} [1 - \frac{1}{4} (7.5)]

- 7.04471 \dots

Solution steps

6 (5) (7.5)^{4} e^{- \frac{5 ( 7.5 )}{4}} [1 - \frac{1}{4} (7.5)]

Apply exponent rule:

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

= 6 \cdot 5 \cdot 7. 5^{4} \cdot \frac{1}{e ^{\frac{5 \cdot 7.5}{4}}} [- 7.5 \cdot \frac{1}{4} + 1]

Multiply the numbers:

5 \cdot 7.5 = 37.5

= 6 \cdot 5 \cdot 7. 5^{4} \cdot \frac{1}{e ^{\frac{37.5}{4}}} (- 7.5 \cdot \frac{1}{4} + 1)

Multiply fractions:

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

= \frac{1 \cdot 6 \cdot 5 \cdot 7. 5 ^{4} ( 1 - \frac{1}{4} \cdot 7.5 )}{e ^{\frac{37.5}{4}}}

Multiply the numbers:

1 \cdot 6 \cdot 5 = 30

= \frac{30 \cdot 7. 5 ^{4} ( - 7.5 \cdot \frac{1}{4} + 1 )}{e ^{\frac{37.5}{4}}}

\frac{1}{4} \cdot 7.5 = 1.875

= \frac{30 \cdot 7. 5 ^{4} ( 1 - 1.875 )}{e ^{\frac{37.5}{4}}}

30 \cdot 7. 5^{4} (1 - 1.875) = - 7. 5^{4} \cdot 26.25

= \frac{- 7. 5 ^{4} \cdot 26.25}{e ^{\frac{37.5}{4}}}

Apply the fraction rule:

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

= - \frac{26.25 \cdot 7. 5 ^{4}}{e ^{\frac{37.5}{4}}}

26.25 \cdot 7. 5^{4} = 83056.640625

= - \frac{83056.640625}{e ^{\frac{37.5}{4}}}

Simplify

\frac{83056.640625}{e ^{\frac{37.5}{4}}} : 7.04471 \dots

= - 7.04471 \dots

(0.4) (44.938 \cdot 1 0^{- 9})

x 1 + \frac{9}{x}

107 (1 + 0.1414)^{- 3}

(7 x^{8}) (6 x^{9}) (8 x^{7})

x^{2} csc (2) (x) d x

What is 6(5)(7.5)^4e^{-(5(7.5))/4}[1-1/4 (7.5)] ?
The solution to 6(5)(7.5)^4e^{-(5(7.5))/4}[1-1/4 (7.5)] is -7.04471…