Solve for x in the equation -5-x-1- -5-5 - -5-7-6721

The correct option is D 1Given, ( 5)^x+1× ( 5)^5 = ( 5)^7. ( 5)^x+1+5=( 5)^7 (∵ a^m × a^n = a^m+n) i.e., ( 5)^x+6 = ( 5)^7 Since the bases are equal, th ...

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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 1
Given, $(- 5)^{x + 1} \times (- 5)^{5} = (- 5)^{7} .$

$⟹ (- 5)^{x + 1 + 5} = (- 5)^{7} (∵ a^{m} \times a^{n} = a^{m + n})$

i.e., $(- 5)^{x + 6} = (- 5)^{7}$

Since the bases are equal, their powers must also be equal.
$∴ x + 6 = 7$
$⟹ x = 1$

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

The correct option is D 1Given, (−5)x+1×(−5)5=(−5)7. ⟹(−5)x+1+5=(−5)7 (∵am×an=am+n) i.e., (−5)x+6=(−5)7 Since the bases are equal, their powers must also be equal. ∴x+6=7 ⟹x=1

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

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

$⟹ (- 5)^{x + 1 + 5} = (- 5)^{7} (∵ a^{m} \times a^{n} = a^{m + n})$

i.e., $(- 5)^{x + 6} = (- 5)^{7}$

Since the bases are equal, their powers must also be equal.
$∴ x + 6 = 7$
$⟹ x = 1$