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Maths-

General

Easy

Question

The expression $fraction numerator x to the power of negative 2 end exponent y to the power of 1 half end exponent over denominator x to the power of 1 third end exponent y to the power of negative 1 end exponent end fraction$ , where x > 1 and y > 1, is equivalent to which of the following?

$\frac{\sqrt{y}}{\sqrt[3]{x^{2}}}$
$\frac{y \sqrt{y}}{\sqrt[3]{x^{2}}}$
$\frac{y \sqrt{y}}{x \sqrt{x}}$
$\frac{y \sqrt{y}}{x^{2} \sqrt[3]{x}}$

The correct answer is: $fraction numerator y square root of y over denominator x squared cube root of x end fraction$

HINT – Use the rule $1 over x to the power of m$ = x^{- m}
SOLUTION – Let the given expression be f(x , y) = $fraction numerator x to the power of negative 2 end exponent y to the power of 1 half end exponent over denominator x to the power of 1 third end exponent y to the power of negative 1 end exponent end fraction$ where x > 1, y > 1
Using the formula, $1 over x to the power of m$ = x^{- m}

We get, f(x , y) = $fraction numerator y to the power of 1 half end exponent y 1 over denominator x squared x to the power of 1 third end exponent end fraction$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals fraction numerator square root of y y over denominator x squared cube root of x end fraction end cell row cell equals fraction numerator y square root of y over denominator x squared cube root of x end fraction end cell end table$
Hence, option D is correct

Related Questions to study

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In the equation above, a, b, c, and d are constants. If the equation has roots −1, −3, and 5, which of the following is a factor of ax³ + bx² + cx + d = 0

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parallel

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