State True or False.
Simplify and express as positive indices:
$(x y)^{m - n} . (y z)^{n - l} . (z x)^{l - m}$ , then the answer is $\frac{x^{l} y^{m} z^{n}}{x^{n} y^{l} z^{m}} = x^{l - n} . y^{m - 1} . z^{n - m}$

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
$(x y)^{m - n} . (y z)^{n - l} . (z x)^{l - m}$
$= x^{(m - n)} y^{(m - n)} . y^{(n - l)} z (n - l) . z^{(l - m)} x^{(l - m)}$
$= \frac{x^{m} y^{m} y^{n} z^{n} z^{l} x^{l}}{x^{n} y^{n} y^{l} z^{l} z^{m} x^{m}}$
$= x^{l - n} . y^{m - 1} . z^{n - m}$

Suggest Corrections

Similar questions

(\frac{32 x^{- 5}}{243 y^{- 5}})^{- \frac{1}{5}}

\frac{3 x}{2 y}

(x^{n} y^{- m})^{4} . \times (x^{3} y^{- 2})^{- n}

\frac{x^{n} y^{2 n}}{y^{4 m}} = x^{n} y^{2 n - 4 m}

{(\frac{125 a^{- 3}}{y^{6}})}^{- \frac{1}{3}}

\frac{a y^{2}}{5}

(a^{- 2} b)^{\frac{1}{2}} \times (a b^{- 3})^{\frac{1}{3}}

\frac{1}{a^{\frac{2}{3}} b^{\frac{1}{2}}}

(a^{- 2} b)^{- 2} \times (a b)^{- 3}

\frac{a}{b^{5}}

Join BYJU'S Learning Program