Question

1) calcule: A) (a^5)²= b) (-2x^4)²= C) (-5y³)³= D) (-10a² b)²= e) (-3x² y)^4= f) (-1/5 m² n)²= g) (0,5a b)²= h) (-a m^5 x³)^4 i) (2/3 x³ y²)^4 j) (a² c³)^7

Answer 1

Oie, Td Bom?!

A)

$= (a {}^{5} ) {}^{2}$

$= a {}^{5 \: . \: 2}$

$= a {}^{10}$

B)

$= ( - 2x {}^{4} ) {}^{2}$

$= ( - 2) {}^{2} \: . \: (x {}^{4} ) {}^{2}$

$= 2 {}^{2} \: . \: x {}^{4 \: . \: 2}$

$= 4x {}^{8}$

C)

$= ( - 5y {}^{3} ) {}^{3}$

$= ( - 5) {}^{3} \: . \: (y {}^{3} ) {}^{3}$

$= - 5 {}^{3} \: . \: y {}^{3 \: . \: 3}$

$= - 125y {}^{9}$

D)

$= ( - 10a {}^{2} b) {}^{2}$

$= (- 10) {}^{2} \: . \: (a {}^{2} ) {}^{2} \: . \: b {}^{2}$

$= 10 {}^{2} \: . \: a {}^{2 \: . \: 2} \: . \: b {}^{2}$

$= 100a {}^{4} b {}^{2}$

E)

$= ( - 3x {}^{2} y ){}^{4}$

$= ( - 3) {}^{4} \: . \: (x {}^{2} ) {}^{4} \: . \: y {}^{4}$

$= - 3 {}^{4} \: . \: x {}^{2 \: . \: 4} \: . \: y {}^{4}$

$= 81x {}^{8} y {}^{4}$

F)

$= ( - \frac{1}{5} m {}^{2} n) {}^{2}$

$= ( - \frac{1}{5} ) {}^{2} \: . \: (m {}^{2} ) {}^{2} \: . \: n {}^{2}$

$= (\frac{1}{5}) {}^{2} \: . \: m {}^{2 \: . \: 2} \: . \: n {}^{2}$

$= \frac{1}{25} m {}^{4} n {}^{2}$

G)

$= (0,5ab) {}^{2}$

$= 0,5 {}^{2} \: . \: a {}^{2} b {}^{2}$

$= \frac{1 {}^{2} }{2 {}^{2} } \: . \: a {}^{2} b {}^{2}$

$= ( \frac{1}{2} ) {}^{2} \: . \: a {}^{2} b {}^{2}$

$= \frac{1}{4} a {}^{2} b {}^{2}$

H)

$= ( - am {}^{5} x {}^{3} ) {}^{4}$

$= ( - a) {}^{4} \: . \: (m {}^{5} ) {}^{4} \: . \: (x {}^{3} ) {}^{4}$

$= ( - a) {}^{4} \: . \: m {}^{5 \: . \: 4} \: . \: n {}^{3 \: . \: 4}$

$= ( - a) {}^{4} \: . \: m {}^{20} \: . \: x {}^{12}$

$= a {}^{4} m {}^{20} x {}^{12}$

I)

$= ( \frac{2}{3} x {}^{3} y {}^{2} ) {}^{2}$

$= ( \frac{2}{3} ) {}^{2} \: . \: (x {}^{3} ) {}^{2} \: . \: (y {}^{2} ){}^{2}$

$= \frac{2 {}^{2} }{3 {}^{2} } \: . \: x {}^{3 \: . \: 2} \: . \: y {}^{2 \: . \: 2}$

$= \frac{4}{9} x {}^{6} y {}^{4}$

J)

$= (a {}^{2} c {}^{3} ) {}^{7}$

$= (a {}^{2} ) {}^{7} \: . \: (c {}^{3} ) {}^{7}$

$= a {}^{2 \: . \: 7} \: . \: c {}^{3 \: . \: 7}$

$= a {}^{14} c {}^{21}$

Att. Makaveli1996