(a^(5)b^(2))/(4b)*(16a^(9)b^(4))/(a^(3)b^(7))

Rewrite as single fraction: First, let's rewrite the expression as a single fraction: \[ \frac{a^5b^2}{4b} \times \frac{16a^9b^4}{a^3b^7} = \frac{a^5b^2 \times 16a^9b^4}{4b \times a^3b^7} \]Simplify constants and powers: Now, simplify the constants and the powers of $a$ and $b$: Constants: $4 \times 16 = 64$, Powers of $a$: $a^{5+9-3} = a^{11}$, Powers of $b$: $b^{2+4-7-1} = b^{-2}$ (Note: The extra -1 in the exponent of $b$ is a mistake). \[ \frac{16a^{11}b^{-2}}{64} \]

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(a^(5)b^(2))/(4b)*(16a^(9)b^(4))/(a^(3)b^(7))

$\frac{a^{5} b^{2}}{4 b} \cdot \frac{16 a^{9} b^{4}}{a^{3} b^{7}}$

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Find derivatives of using multiple formulae

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\frac{a^{5} b^{2}}{4 b} \cdot \frac{16 a^{9} b^{4}}{a^{3} b^{7}}

Rewrite as single fraction: First, let's rewrite the expression as a single fraction: $\newline$ $\frac{a^5b^2}{4b} \times \frac{16a^9b^4}{a^3b^7} = \frac{a^5b^2 \times 16a^9b^4}{4b \times a^3b^7}$
Simplify constants and powers: Now, simplify the constants and the powers of $a$ and $b$ : $\newline$ Constants: $4 \times 16 = 64$ , $\newline$ Powers of $a$ : $a^{5+9-3} = a^{11}$ , $\newline$ Powers of $b$ : $b^{2+4-7-1} = b^{-2}$ (Note: The extra $-1$ in the exponent of $b$ is a mistake). $\newline$ $\frac{16a^{11}b^{-2}}{64}$