What is (1/2 a^2)(4/5 a^3b) ?

The solution to (1/2 a^2)(4/5 a^3b) is (2a^5b)/5

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simplify (1/2 a^2)(4/5 a^3b)

simplify

(\frac{1}{2} a^{2}) (\frac{4}{5} a^{3} b)

\frac{2 a ^{5} b}{5}

Solution steps

(\frac{1}{2} a^{2}) (\frac{4}{5} a^{3} b)

Apply exponent rule:

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

a^{2} a^{3} = a^{2 + 3}

= \frac{1}{2} \cdot \frac{4}{5} a^{2 + 3} b

Add the numbers:

2 + 3 = 5

= \frac{1}{2} \cdot \frac{4}{5} a^{5} b

Multiply fractions:

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

= \frac{1 \cdot 4 a ^{5} b}{2 \cdot 5}

Refine

= \frac{4 a ^{5} b}{10}

Cancel the common factor:

2

= \frac{2 a ^{5} b}{5}

e^{- 3 \cdot (1 - 0.67) 0.25}

0.05 \cdot 40 \cdot 1 0^{- 9} \frac{1}{100}

e^{(- \frac{- 6.7}{8.314 \cdot 298.15})}

(3 a^{3} b^{3}) (4 a b^{2})

a \cdot e^{- x}