What is ((9c^4)/(5c))^3 ?

The solution to ((9c^4)/(5c))^3 is (729c^9)/(125)

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simplify ((9c^4)/(5c))^3

simplify

(\frac{9 c ^{4}}{5 c})^{3}

\frac{729 c ^{9}}{125}

Solution steps

(\frac{9 c ^{4}}{5 c})^{3}

Apply exponent rule:

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

= \frac{( 9 c ^{4} ) ^{3}}{( 5 c ) ^{3}}

Simplify

(9 c^{4})^{3} : 729 c^{12}

= \frac{729 c ^{12}}{( 5 c ) ^{3}}

Simplify

(5 c)^{3} : 125 c^{3}

= \frac{729 c ^{12}}{125 c ^{3}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{c ^{12}}{c ^{3}} = c^{12 - 3}

= \frac{729 c ^{12 - 3}}{125}

Subtract the numbers:

12 - 3 = 9

= \frac{729 c ^{9}}{125}

x^{2} = 5 - x

(\frac{- 1}{2})^{2}

3 x^{2} - 2 x - 12 = 0

8 (5) - 2 (9) < - 12

(x - 2)^{2} (x - 5) < 0