What is e^{-2}x^5x^{0.3} ?

The solution to e^{-2}x^5x^{0.3} is 0.13533…x^{5.3}

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simplify e^{-2}x^5x^{0.3}

simplify

e^{- 2} x^{5} x^{0.3}

0.13533 \dots x^{5.3}

Solution steps

e^{- 2} x^{5} x^{0.3}

Apply exponent rule:

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

x^{5} x^{0.3} = x^{5 + 0.3}

= e^{- 2} x^{5 + 0.3}

Add the numbers:

5 + 0.3 = 5.3

= e^{- 2} x^{5.3}

Apply exponent rule:

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

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

= \frac{1}{e ^{2}} x^{5.3}

Multiply fractions:

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

= \frac{1 \cdot x ^{5.3}}{e ^{2}}

Multiply:

1 \cdot x^{5.3} = x^{5.3}

= \frac{x ^{5.3}}{e ^{2}}

Convert element to a decimal form

e^{2} = 7.38905 \dots

= \frac{x ^{5.3}}{7.38905 \dots}

Divide the numbers:

\frac{1}{7.38905 \dots} = 0.13533 \dots

= 0.13533 \dots x^{5.3}

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