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

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

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simplify (1/2 a^2b)*(2/5 ab^3)

simplify

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

\frac{a ^{3} b ^{4}}{5}

Solution steps

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

Apply exponent rule:

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

a^{2} a = a^{2 + 1}

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

Add the numbers:

2 + 1 = 3

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

Apply exponent rule:

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

b b^{3} = b^{1 + 3}

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

Add the numbers:

1 + 3 = 4

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

Multiply fractions:

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

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

Cancel the common factor:

2

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

Multiply:

1 \cdot a^{3} = a^{3}

= \frac{a ^{3} b ^{4}}{5}

\frac{2. 5 ^{- 4}}{7. 5 ^{- 4}}

(4 b^{3}) (8 b^{2})

(2 a^{2}) (8 a)

x \cdot 5

What is (1/2 a^2b)*(2/5 ab^3) ?
The solution to (1/2 a^2b)*(2/5 ab^3) is (a^3b^4)/5