What is (6^2)^4*9^3*((2^6)/(2^4))' ?

The solution to (6^2)^4*9^3*((2^6)/(2^4))' is 12244400644'

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simplify (6^2)^49^3((2^6)/(2^4))'

simplify

(6^{2})^{4} \cdot 9^{3} \cdot (\frac{2 ^{6}}{2 ^{4}})^{'}

12244400644'

Solution steps

(6^{2})^{4} \cdot 9^{3} (\frac{2 ^{6}}{2 ^{4}})^{'}

(6^{2})^{4} : 6^{8}

= 6^{8} \cdot 9^{3} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Factor integer

6 = 3 \cdot 2

= (3 \cdot 2)^{8} \cdot 9^{3} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(3 \cdot 2)^{8} = 3^{8} \cdot 2^{8}

= 3^{8} \cdot 2^{8} \cdot 9^{3} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Factor integer

9 = 3^{2}

= 3^{8} \cdot 2^{8} (3^{2})^{3} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(3^{2})^{3} = 3^{2 \cdot 3}

= 3^{8} \cdot 2^{8} \cdot 3^{2 \cdot 3} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Refine

= 3^{8} \cdot 2^{8} \cdot 3^{6} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Apply exponent rule:

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

3^{8} \cdot 3^{6} = 3^{8 + 6}

= 2^{8} \cdot 3^{8 + 6} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Add the numbers:

8 + 6 = 14

= 2^{8} \cdot 3^{14} (\frac{2 ^{6}}{2 ^{4}})^{^{'}}

Cancel

\frac{2 ^{6}}{2 ^{4}} : 2^{2}

= 3^{14} \cdot 2^{8} (2^{2})^{'}

Refine

= 1224440064 4^{^{'}}

π (e^{- 2 x})^{2}

2 \cdot 3 \cdot 1 0^{- 4} \cdot e^{- \frac{1}{10}} \cdot 1 0^{- 2}

e^{- \frac{0}{1}}

4 π \cdot 1 0^{- 7} \cdot (2.4 \cdot 1 0^{- 3})

4 π^{2} (1.8 s^{- 1})^{2} [1130 k g + 4 (72.4 k g)]

What is (6^2)^4*9^3*((2^6)/(2^4))' ?
The solution to (6^2)^4*9^3*((2^6)/(2^4))' is 12244400644'