Question

${\huge{\boxed{\bf{\mathtt {question}}}}}$
Find the value of "x"

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Answer 1

• Question

$: \implies$ $\sf{\bigg(\dfrac{1}{5}\bigg)^{-3} \times \bigg(\dfrac{1}{5}\bigg)^{-5} = \bigg(\dfrac{1}{5}\bigg)^{x}}$

• Solution

$\implies\sf{\bigg(\dfrac{1}{5}\bigg)^{-3} \times \bigg(\dfrac{1}{5}\bigg)^{-5} = \bigg(\dfrac{1}{5}\bigg)^{x}}$

$\implies\sf{\bigg(\dfrac{1}{5}\bigg)^{-3 +( - 5)} = \bigg(\dfrac{1}{5}\bigg)^{x}}$

$\implies\sf{\bigg(\dfrac{1}{5}\bigg)^{-3- 5} = \bigg(\dfrac{1}{5}\bigg)^{x}}$

$\implies\sf{\bigg(\dfrac{1}{5}\bigg)^{-8} = \bigg(\dfrac{1}{5}\bigg)^{x}}$

$\red{\bigstar}$ Bases are equal, powers are equal.

$\implies\sf{ - 8 = x}$

$\red{\bigstar}$ $\large{\boxed{\sf{\blue{x = - 8}}}}$

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• Know MorE -

$\red{\bigstar}$ Laws of Indices -

$\red{\bigstar}$ 1st Law (Product Law)

• For example -
• $:  \implies\sf{ {a}^{2} \times  {a}^{3} =  {a}^{2 + 3}   }$
• $:  \implies\sf{ {a}^{5}   }$

$\red{\bigstar}$ 2nd Law  (Quotient law)

For example -

$: \implies\sf{ \dfrac{a^{2} }{a^{3}} }$

$: \implies\sf{a^{2 - 3} }$

$: \implies\sf{a^{ - 1} }$

$\red{\bigstar}$ 3rd Law (Quotient law)

For example -

$: \implies\sf{(a^2)^3}$

$: \implies\sf{(a^{2 \times 3})}$

$: \implies\sf{(a^{6})}$

Answer 2

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