Question

Which expression is equivalent to StartFraction negative 9 x Superscript negative 1 Baseline y Superscript negative 9 Baseline Over negative 15 x Superscript 5 Baseline y Superscript negative 3 Baseline EndFraction? Assume x not-equals 0, y not-equals 0.
StartFraction 3 Over 5 x Superscript 5 Baseline y cubed EndFraction
StartFraction 3 Over 5 x Superscript 6 Baseline y Superscript 6 Baseline EndFraction
StartFraction 5 Over 3 x Superscript 5 Baseline y cubed EndFraction
StartFraction 5 Over 3 x Superscript 6 Baseline y Superscript 6 Baseline EndFraction

Answer 1

GIVEN :

The expression is Start Fraction negative 9 x Superscript negative 1 Baseline y Superscript negative 9 Baseline Over negative 15 x Superscript 5 Baseline y Superscript negative 3 Baseline End Fraction.

TO FIND :

The equivalent expression to the given expression

SOLUTION :

Assume that $x\neq 0$ and $y\neq 0$

The given expression can be written as

$\frac{-9x^{-1}.y^{-9}}{-15x^5.y^{-3}}$

To simplify the given expression as below:

$\frac{-9x^{-1}.y^{-9}}{-15x^5.y^{-3}}$

$=\frac{3x^{-1}.y^{-9}}{5x^5.y^{-3}}$

By using the identity:

$a^{-m}=\frac{1}{a^m}$

$=\frac{3}{5x^5.y^{-3}.x^1.y^9}$

$=\frac{3}{5x^5.x^1.y^{-3}.y^9}$

By using the identities:

$a^m.a^n=a^{m+n}$

$a^m.a^{-n}=a^{m-n}$

$=\frac{3}{5x^{5+1}.y^{-3+9}}$

$=\frac{3}{5x^6.y^6}$

$\frac{-9x^{-1}.y^{-9}}{-15x^5.y^{-3}}=\frac{3}{5x^6.y^6}$ for $x\neq 0$ and $y\neq 0$

The equivalent expression to the given expression $\frac{-9x^{-1}.y^{-9}}{-15x^5.y^{-3}}$ is $\frac{3}{5x^6.y^6}$ for $x\neq 0$ and $y\neq 0$

∴ option b) Start Fraction 3 Over 5 x Superscript 6 Baseline y Superscript 6 Baseline End Fraction is correct

That is $\frac{3}{5x^6.y^6}$ for $x\neq 0$ and $y\neq 0$ is correct.

Answer 2

Answer:  $\frac{3 }{5x^{6} y^{6} }$

Step-by-step explanation:

• Given: $\frac{-9x^{-1}y^{-9} }{-15x^{5}y^{-3} }$ where x≠0.
• To find: Simplify and tick the correct option.
• Solution:

        We know, any number with negative power can be written in inverse form with positive power.

    $x^{-a}=\frac{1}{x^{a} }$

Two number having same base their powers are added.

$x^{a}+x^{b}=x^{a+b}$

Now,  $\frac{-9x^{-1}y^{-9} }{-15x^{5}y^{-3} }$ $=\frac{3x^{-1}y^{-9} }{5x^{5}y^{-3} }$

                        $=\frac{3 }{5x^{5}x^{1} y^{-3}y^{9} }$

                        $=\frac{3 }{5x^{6} y^{6} }$

• Hence, the required answer is  $\frac{3 }{5x^{6} y^{6} }$.

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