What is ((12p^{3/2})/(15p))^4 ?

The solution to ((12p^{3/2})/(15p))^4 is (256p^2)/(625)

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simplify ((12p^{3/2})/(15p))^4

simplify

(\frac{12 p ^{\frac{3}{2}}}{15 p})^{4}

\frac{256 p ^{2}}{625}

Solution steps

(\frac{12 p ^{\frac{3}{2}}}{15 p})^{4}

Apply exponent rule:

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

= \frac{( 12 p ^{\frac{3}{2}} ) ^{4}}{( 15 p ) ^{4}}

Simplify

(12 p^{\frac{3}{2}})^{4} : 20736 p^{6}

= \frac{20736 p ^{6}}{( 15 p ) ^{4}}

Simplify

(15 p)^{4} : 50625 p^{4}

= \frac{20736 p ^{6}}{50625 p ^{4}}

Cancel the common factor:

81

= \frac{256 p ^{6}}{625 p ^{4}}

Apply exponent rule:

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

\frac{p ^{6}}{p ^{4}} = p^{6 - 4}

= \frac{256 p ^{6 - 4}}{625}

Subtract the numbers:

6 - 4 = 2

= \frac{256 p ^{2}}{625}

3 (4 x + 4) = 2 (5 x + 9) - 12

9 x^{2} - 6 x y - 8 y^{2}

\frac{3}{2} + \frac{5}{4} + \frac{9}{8} + \frac{17}{16} + \frac{33}{32} + \frac{65}{64} - 7

2 x = 4 x + 4

\frac{c}{2} - 1 \geq 1

What is ((12p^{3/2})/(15p))^4 ?
The solution to ((12p^{3/2})/(15p))^4 is (256p^2)/(625)