What is (8x^{10}e^{-7})(6.2x10^2) ?

The solution to (8x^{10}e^{-7})(6.2x10^2) is 4.52293…x^{11}

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simplify (8x^{10}e^{-7})(6.2x10^2)

simplify

(8 x^{10} e^{- 7}) (6.2 x 1 0^{2})

4.52293 \dots x^{11}

Solution steps

(8 x^{10} e^{- 7}) (6.2 x \cdot 1 0^{2})

Apply exponent rule:

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

x^{10} x = x^{10 + 1}

= 8 e^{- 7} \cdot 6.2 x^{10 + 1} \cdot 1 0^{2}

Add the numbers:

10 + 1 = 11

= 8 e^{- 7} \cdot 6.2 x^{11} \cdot 1 0^{2}

Apply exponent rule:

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

e^{- 7} = \frac{1}{e ^{7}}

= 1 0^{2} \cdot 8 \cdot 6.2 \cdot \frac{1}{e ^{7}} x^{11}

Multiply fractions:

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

= 6.2 \cdot \frac{1 0 ^{2} \cdot 1 \cdot 8 x ^{11}}{e ^{7}}

Simplify

\frac{1 \cdot 8 x ^{11} \cdot 1 0 ^{2}}{e ^{7}} : \frac{800 x ^{11}}{e ^{7}}

= 6.2 \cdot \frac{800 x ^{11}}{e ^{7}}

Multiply fractions:

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

= \frac{800 x ^{11} \cdot 6.2}{e ^{7}}

Multiply the numbers:

800 \cdot 6.2 = 4960

= \frac{4960 x ^{11}}{e ^{7}}

Convert element to a decimal form

e^{7} = 1096.63315 \dots

= \frac{4960 x ^{11}}{1096.63315 \dots}

Divide the numbers:

\frac{4960}{1096.63315 \dots} = 4.52293 \dots

= 4.52293 \dots x^{11}

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What is (8x^{10}e^{-7})(6.2x10^2) ?
The solution to (8x^{10}e^{-7})(6.2x10^2) is 4.52293…x^{11}