What is 4000(1+0.03)^{-65/2} ?

The solution to 4000(1+0.03)^{-65/2} is (4.0E68)/(103^{65/2)}

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simplify 4000(1+0.03)^{-65/2}

simplify

4000 (1 + 0.03)^{- \frac{65}{2}}

\frac{4.0 E 68}{10 3 ^{\frac{65}{2}}}

Decimal Notation

1530.55939 \dots

Solution steps

4000 (1 + 0.03)^{- \frac{65}{2}}

Apply exponent rule:

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

(1 + 0.03)^{- \frac{65}{2}} = \frac{1}{( 1 + 0.03 ) ^{\frac{65}{2}}}

= 4000 \cdot \frac{1}{( 1 + 0.03 ) ^{\frac{65}{2}}}

(1 + 0.03)^{\frac{65}{2}} = \frac{10 3 ^{32} \cdot 10 3 ^{\frac{1}{2}}}{1.0 E 65}

= 4000 \cdot \frac{1}{\frac{10 3 ^{32} \cdot 10 3 ^{\frac{1}{2}}}{1.0 E 65}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= 4000 \cdot \frac{1.0 E 65}{10 3 ^{32} \cdot 10 3 ^{\frac{1}{2}}}

10 3^{32} \cdot 10 3^{\frac{1}{2}} = 10 3^{\frac{65}{2}}

= 4000 \cdot \frac{1.0 E 65}{10 3 ^{\frac{65}{2}}}

4000 \cdot \frac{1.0 E 65}{10 3 ^{\frac{65}{2}}} = \frac{4.0 E 68}{10 3 ^{\frac{65}{2}}}

= \frac{4.0 E 68}{10 3 ^{\frac{65}{2}}}

a e^{- s i n (x)} e^{- s i n (x)}

e^{- 0.4 \cdot 10000}

7.29 \cdot 1 0^{- 4}

e^{- 2 (l n (7))}

3 x + 7

What is 4000(1+0.03)^{-65/2} ?
The solution to 4000(1+0.03)^{-65/2} is (4.0E68)/(103^{65/2)}