Solve for x in the equation -5 x -1-5-5-5-7-A- -6B- 4C- 5D- -3

The correct option is D 3Given, ( 5)^x+1× ( 5)^ 5 = ( 5)^ 7 We know, a^m × a^n = a^m+n ⇒ ( 5)^x+1 5=( 5)^ 7 i.e., ( 5)^x 4 = ( 5)^ 7 Since the bases are e ...

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Standard VII

Mathematics

Product Rule of Exponents

Solve for x i...

Question

Solve for $x$ in the equation $(- 5)^{x + 1} \times (- 5)^{- 5} = (- 5)^{- 7}$ .

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Solution

The correct option is D -3
Given, $(- 5)^{x + 1} \times (- 5)^{- 5} = (- 5)^{- 7}$

We know, $a^{m} \times a^{n} = a^{m + n}$

$\Rightarrow (- 5)^{x + 1 - 5} = (- 5)^{- 7}$
i.e., $(- 5)^{x - 4} = (- 5)^{- 7}$

Since the bases are equal, their exponents must also be equal.
$∴ x - 4 = - 7$
$\Rightarrow x = - 7 + 4 = - 3$

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Solve for x in the equation (−5)x+1×(−5)−5=(−5)−7.

The correct option is D -3Given, (−5)x+1×(−5)−5=(−5)−7 We know, am×an=am+n ⇒(−5)x+1−5=(−5)−7 i.e., (−5)x−4=(−5)−7 Since the bases are equal, their exponents must also be equal. ∴x−4=−7 ⇒x=−7+4=−3

Solve for $x$ in the equation $(- 5)^{x + 1} \times (- 5)^{- 5} = (- 5)^{- 7}$ .