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semplificare ((5a^2b^{-8}c)/(25ab^0c^6))^3

Soluzione

semplificare

(\frac{5 a ^{2} b ^{- 8} c}{25 a b ^{0} c ^{6}})^{3}

\frac{a ^{3}}{125 b ^{24} c ^{15}}

Fasi della soluzione

(\frac{5 a ^{2} b ^{- 8} c}{25 a b ^{0} c ^{6}})^{3}

Applica la regola degli esponenti:

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

= \frac{( 5 a ^{2} b ^{- 8} c ) ^{3}}{( 25 a b ^{0} c ^{6} ) ^{3}}

Semplificare

(5 a^{2} b^{- 8} c)^{3} : \frac{125 a ^{6} c ^{3}}{b ^{24}}

= \frac{\frac{125 a ^{6} c ^{3}}{b ^{24}}}{( 25 a b ^{0} c ^{6} ) ^{3}}

Semplificare

(25 a b^{0} c^{6})^{3} : 15625 a^{3} c^{18}

= \frac{\frac{125 a ^{6} c ^{3}}{b ^{24}}}{15625 a ^{3} c ^{18}}

Applica la regola delle frazioni:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{125 a ^{6} c ^{3}}{b ^{24} \cdot 15625 a ^{3} c ^{18}}

Cancella il fattore comune:

125

= \frac{a ^{6} c ^{3}}{125 a ^{3} b ^{24} c ^{18}}

Applica la regola degli esponenti:

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

\frac{a ^{6}}{a ^{3}} = a^{6 - 3}

= \frac{c ^{3} a ^{6 - 3}}{125 b ^{24} c ^{18}}

Sottrai i numeri:

6 - 3 = 3

= \frac{a ^{3} c ^{3}}{125 b ^{24} c ^{18}}

Applica la regola degli esponenti:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{c ^{3}}{c ^{18}} = \frac{1}{c ^{18 - 3}}

= \frac{a ^{3}}{125 b ^{24} c ^{18 - 3}}

Sottrai i numeri:

18 - 3 = 15

= \frac{a ^{3}}{125 b ^{24} c ^{15}}

f a c t or 4 x - 3 x^{2}

s im pl i f y 490 y^{5} w^{6}

s im pl i f y \frac{5}{6} \cdot \frac{4}{15} - \frac{3}{5} \cdot \frac{20}{18}

e x p an d (2 n + 3)^{3}

s im pl i f y (2 x x^{2} + 1)^{2}