Question

(i) a⁵b²/a²b-³

(ii) 15y⁸ ÷ 3y³

(iii) x¹⁰y⁶÷ x³y-²

(iv) 5z¹⁶ + 15z-¹¹


(v) (36x²)^½

(vi) (125x-³)^⅓

(vii)(2x²y-³)-²

(viii) (27x-³y⁶)^2/3

(ix)(-2x^2/3y^-3/2)⁶​

Answer 1

$\huge\underline\red{\boxed{\bf •Answer•}}$

(i) a⁵b²/a²b-³

=a⁵-².b²+³

=a³b⁵

(ii) 15y⁸ ÷ 3y³

$= \frac{15y {}^{8} }{3y {}^{3} }$

=5y⁸-³

=5y⁵

(iii) x¹⁰y⁶÷ x³y-²

$= \frac{x {}^{10} y {}^{6} }{x {}^{3} y {}^{ - 2} }$

=x¹⁰-³.y⁶+²

= x⁷y⁸

(iv) 5z¹⁶ + 15z-¹¹⁶

$= \frac{5 {z}^{16} }{15z ^{ - 11} }$

$= \frac{5}{15} z ^{16 + 11}$

$= \frac{1}{3} {z}^{27}$

(v) (36x²)^½

$= ({36})^{\frac{1}{2} } .x^{2 \times } { }^{\frac{1}{2}}$

$=(6×6){ \frac{1}{2} } .x$

$= (6 {}^{2} ) {}^{ \frac{1}{2} } .x$

$= 6x$

(vi) (125x-³)^⅓

$= (125) ^{ \frac{1}{3} } .x { }^{ - 3 \times \frac{1}{3} }$

$= (5 \times 5 \times 5) {}^{\frac{1}{3} } .x {}^{ - 1}$

$= (5 {}^{3} ) {}^{ \frac{1}{3} } .x {}^{ - 1}$

$= 5x {}^{ - 1}$

$= \frac{5}{x}$

$= 5x {}^{ - 1}$

(vii)(2x²y-³)-²

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

$= \frac{1}{2 {}^{2} }x {}^{- 4} .y {}^{6}$

$= \frac{1}{4} \times \frac{y {}^{6} }{x {}^{4} }$

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

$= \frac{1}{4} .y {}^{6} .x {}^{ - 4}$

(viii) (27x-³y⁶)^2/3

$= {27}^{ \frac{2}{3} } .x { }^{ - 3 \times \frac{2}{3} } .y {}^{6 \times \frac{2}{3} }$

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

$= [(3 \times 3 \times 3) {}^{ \frac{1}{3} } ] {}^{2} .x {}^{ - 2} .y {}^{4}$

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

$= 9x {}^{ - 2} .y {}^{4}$

$= \frac{9y {}^{4} }{x {}^{2} }$

$= 9x {}^{ - 2} .y {}^{4}$

(ix)(-2x^2/3y^-3/2)

$= ( - 2) {}^{6} .x {}^{ \frac{2}{3 } } {}^{ \times 6} .y {}^{ \frac{ - 3}{2} } {}^{ \times 6}$

$= 64x {}^{4} y {}^{ - 9}$

$= \frac{ 64x {}^{4}}{ {y}^{ - 9} }$

$= 64x {}^{4} y {}^{ - 9}$