Math, asked by RichWeedx, 4 months ago

Find k if x^k-1=(x^2)^-2/x^3
Someone please answer it :) thx
pleaseee​

Answers

Answered by Steph0303
32

Answer:

  • k = (-6)

Steps:

\text{Given:}\:\:\: x^{k-1} = \dfrac{(x^2)^{-2}}{x^3}

From the identities of laws of exponents we know:

\boxed{\bf{ \dfrac{x^{a}}{x^{b}} = x^{a-b}}}

Using this, we can simplify the RHS. On simplifying we get:

\implies x^{k-1} = \dfrac{(x^2)^{-2}}{x^3} = \dfrac{(x^{2 \times (- 2)})}{x^3}\\\\\\\implies x^{k-1} = \dfrac{x^{-4}}{x^3}\\\\\\\text{Using the identity we get,}\\\\\\\implies x^{k-1} = x^{(-4 - 3)}\\\\\\\implies \boxed{ \bf{ x^{k-1} = x^{-7}}}

Since the bases are equal, we can equate the powers. Hence we get:

→ k - 1 = -7

→ k = -7 + 1

k = -6

Hence the value of 'k' is equal to (-6).

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