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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Add the numbers:

2 + 3 = 5

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

Apply exponent rule:

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

b b^{4} = b^{1 + 4}

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

Add the numbers:

1 + 4 = 5

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

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 ^{5}}{2 \cdot 5}

Refine

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

Cancel the common factor:

2

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

4 π \cdot 1 0^{- 12}

e^{- s t} \cdot t \cdot e^{a t}

e^{s - t} \cdot e^{s + t}

(25 - 4 x)^{- \frac{1}{2}}

(3 x^{2}) (6 x^{4})

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