Simplify - -i-a-5b-2-a-2b-3-ii-15y-8-3y-3-iii-x-10y-6- x-3y-2-iv-5z-16-15z-11-v-36x-2-1-2-vi-125x-3-1-3-vii-2x-2y-3-2-viii-27x-3y-6-2-3-ix-2x-2-3y-3-2 -6

(i) a^5b^2/a^2b^ 3=a^5 2.b^2+3 =a^3b^5. (ii) 15y^8÷3y^3=16y^8/3y^3 =5y^8 3 =5y^5. (iii) x^10y^6÷ x^3y^ 2=x^10y^6/x^3y^ 2 =x^1 ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with Unlike Bases and Same Exponent

Simplify : (i...

Question

Simplify :

$(i) \frac{a^{5} b^{2}}{a^{2} b^{- 3}} (i i) 15 y^{8} \div 3 y^{3} (i i i) x^{10} y^{6} \div x^{3} y^{- 2} (i v) 5 z^{16} \div 15 z^{- 11} (v) (36 x^{2})^{\frac{1}{2}} (v i) (125 x^{- 3})^{\frac{1}{3}} (v i i) (2 x^{2} y^{- 3})^{- 2} (v i i i) (27 x^{- 3} y^{6})^{\frac{2}{3}} (i x) {(- 2 x^{\frac{2}{3}} y^{- \frac{3}{2}})}^{6}$

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Solution

$(i) \frac{a^{5} b^{2}}{a^{2} b^{- 3}} = a^{5 - 2} . b^{2 + 3} = a^{3} b^{5} . (i i) 15 y^{8} \div 3 y^{3} = \frac{16 y^{8}}{3 y^{3}} = 5 y^{8 - 3} = 5 y^{5} . (i i i) x^{10} y^{6} \div x^{3} y^{- 2} = \frac{x^{10} y^{6}}{x^{3} y^{- 2}} = x^{10 - 3} . y^{6 + 2} = x^{7} y^{8} (i v) 5 z^{16} \div 15 z^{- 11} = \frac{5 z^{16}}{15 z^{- 11}} = \frac{5}{15} z^{16 + 11} = \frac{1}{3} z^{27} (v) (36 x^{2})^{\frac{1}{2}} = (36)^{\frac{1}{2}} . x^{2 \times \frac{1}{2}} = (6 \times 6)^{\frac{1}{2}} . x = (6^{2})^{\frac{1}{2}} . x = 6 x (v i) (125 x^{- 3})^{\frac{1}{3}} = (125)^{\frac{1}{3}} . x^{- 3 \times \frac{1}{3}} = (5 \times 5 \times 5)^{\frac{1}{3}} . x^{- 1} (5^{3})^{\frac{1}{3}} . x^{- 1} = 5 x^{- 1} = \frac{5}{x} = 5 x^{- 1} (v i i) (2 x^{2} y^{- 3})^{- 2} = 2^{- 2} . x^{2 \times - 2} . y^{- 3 \times - 2} = \frac{1}{2^{2}} x^{- 4} . y^{6} = \frac{1}{4} \times \frac{y^{6}}{x^{4}} = \frac{y^{6}}{4 x^{4}} = \frac{1}{4} . y^{6} . x^{- 4} (v i i i) (27 x^{- 3} y^{6})^{\frac{2}{3}} = (27)^{\frac{2}{3}} . x^{- 3 \times \frac{2}{3}} . y^{6 \times \frac{2}{3}} = (3 \times 3 \times 3)^{\frac{2}{3}} . x^{- 2} . y^{4} = [(3 \times 3 \times 3)^{\frac{1}{3}}]^{2} . x^{- 2} . y^{4} = 3^{2} . x^{- 2} y^{4} = 9 x^{- 2} y^{4} = \frac{9 y^{4}}{x^{2}} = 9 x^{- 2} y^{4} (i x) {(- 2 x^{\frac{2}{3}} y^{- \frac{3}{2}})}^{6} = (- 2)^{6} . x^{\frac{2}{3} \times 6} . y^{- \frac{3}{2} \times 6} = 64 x^{4} y^{- 9} = \frac{64 x^{4}}{y^{9}} = 64 x^{4} y^{- 9}$

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Similar questions

Q. Find the principal values of each of the following:
(i)

\tan^{- 1} (- \sqrt{3})

(ii)

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

(iii)

{cosec}^{- 1} (- \sqrt{2})

(iv)

\cos^{- 1} (- \frac{\sqrt{3}}{2})

(v)

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

(vi)

\tan^{- 1} (\frac{1}{\sqrt{3}})

(vii)

\sec^{- 1} (- \sqrt{2})

(viii)

\cot^{- 1} (- \sqrt{3})

(ix)

\sec^{- 1} (2)

(x)

{cosec}^{- 1} (\frac{2}{\sqrt{3}})

Q. State True or False.

Simplifying

(27 x^{- 3} y^{6})^{\frac{2}{3}}

, we get

9 x^{- 2} y^{4}

Q. State True or False.

Simplify:

\frac{a^{5} b^{2}}{a^{2} b^{- 3}}

, then answer is

a^{3} b^{5}

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

(ii) $y^{3} + \sqrt{3} y$

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

(vi) $x^{- 2} + 2 x^{- 1} + 3$

(vii) $1$

(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

(xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$

(xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$

(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

(xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

Q. State True or False.

Simplify:

x^{10} y^{6} \div x^{3} y^{- 2}

, then answer is

x^{7} y^{8}

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Simplify : (i) a5b2a2b−3(ii) 15y8÷3y3(iii) x10y6÷x3y−2(iv) 5z16÷15z−11(v) (36x2)12(vi) (125x−3)13(vii) (2x2y−3)−2(viii) (27x−3y6)23(ix) (−2x23y−32)6