It is given that xyz- yx-5- Find the value of z-

Given: nbsp; (xy)^z= (yx)^ 5 To Find: nbsp; Value of z (xy)^z= (yx)^ 5 Applying the exponent rule (ab)^ n=(ba)^n on R.H.S of the equation to remove the n ...

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Standard VIII

Mathematics

Powers with Negative Exponents

It is given t...

Question

It is given that $(\frac{x}{y})^{z} = (\frac{y}{x})^{- 5}$ . Find the value of $z$ .

- 5

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Solution

The correct option is B $5$
Given: $(\frac{x}{y})^{z} = (\frac{y}{x})^{- 5}$

To Find: Value of $z$

$(\frac{x}{y})^{z} = (\frac{y}{x})^{- 5}$

Applying the exponent rule $(\frac{a}{b})^{- n} = (\frac{b}{a})^{n}$ on R.H.S of the equation to remove the negative sign from the exponent.

$\Rightarrow (\frac{x}{y})^{z} = (\frac{x}{y})^{5}$

Here, as bases are same, the exponents on both the sides must also be the same for the equality.

$\Rightarrow z = 5$

Therefore, option (b.) is the correct one.

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It is given that (xy)z=(yx)−5. Find the value of z.

It is given that $(\frac{x}{y})^{z} = (\frac{y}{x})^{- 5}$ . Find the value of $z$ .