Simplified form of -x4y-1-x2 y8 -6

The correct option is A y^10/x^5 [ (x^4.y)^1/3 . #160;1/(x^2.y^3)^1/4 ]^ 6 = [ x^4/3.y^1/3 × #160;1/(x^2/4.y^3/4) ]^ 6 = [ x^4/3 1/2 ...

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Byju's Answer

Standard VII

Mathematics

Power Law

Simplified fo...

Question

Simplified form of
${[\sqrt[3]{x^{4} y} \times \frac{1}{\sqrt[4]{x^{2} y^{8}}}]}^{- 6}$

x^{5} . y^{10}

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\frac{y^{10}}{x^{5}}

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\frac{y^{2}}{x}

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\frac{y^{5}}{x^{5}}

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Solution

The correct option is A $\frac{y^{10}}{x^{5}}$
${⎡ ⎢ ⎣ (x^{4} . y)^{\frac{1}{3}} . \frac{1}{(x^{2} . y^{8})^{\frac{1}{4}}} ⎤ ⎥ ⎦}^{- 6}$
$= {⎡ ⎢ ⎣ x^{\frac{4}{3}} . y^{\frac{1}{3}} \times \frac{1}{(x^{\frac{2}{4}} . y^{\frac{8}{4}})} ⎤ ⎥ ⎦}^{- 6}$
$= {[x^{\frac{4}{3} - \frac{1}{2}} \times y^{\frac{1}{3} - 2}]}^{- 6} = {[x^{\frac{8 - 3}{6}} . y^{\frac{1 - 6}{3}}]}^{- 6}$
$= (x^{\frac{5}{6}} . y^{- \frac{5}{3}})^{- 6} = x^{\frac{5}{6} \times - 6} . y^{- \frac{5}{3} \times - 6}$
$= x^{- 5} \times y^{+ 10} = \frac{y^{10}}{x^{5}}$

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Similar questions

Question 4

For any non-zero rational numbers $x$ and $y$ , $x^{5} \div y^{5}$ is equal to
(a) $(x \div y)^{1}$
(b) $(x \div y)^{0}$
(c) $(x \div y)^{5}$
(d) $(x \div y)^{10}$

Q. Simplify:

\frac{x^{5} y^{3} - x^{3} y^{5}}{x^{3} y^{3}}

Q. Write the degree of each of the following polynomials:

x^{5} y^{6} - 7 x^{3} y^{10} + 20 x^{5} y^{6} z^{5}

The expansion of (x + 2y)⁵ by using binomial theorem is

Q. Simplify:

x^{2} \times y^{2} \times x^{5} \times y^{3}

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Simplified form of[3√x4y×14√x2y8]−6

The correct option is A y10x5⎡⎢⎣(x4.y)13.1(x2.y8)14⎤⎥⎦−6=⎡⎢⎣x43.y13×1(x24.y84)⎤⎥⎦−6=[x43−12×y13−2]−6=[x8−36.y1−63]−6=(x56.y−53)−6=x56×−6.y−53×−6=x−5×y+10=y10x5

Simplified form of
${[\sqrt[3]{x^{4} y} \times \frac{1}{\sqrt[4]{x^{2} y^{8}}}]}^{- 6}$