Find the value of x in the following equation-5x-1- -55 - -57

Given, ( 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, their powers must also ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with like Bases

Find the valu...

Question

Find the value of $x$ in the following 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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Find the value of x in the following 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

Find the value of $x$ in the following 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.
$∴ x + 6 = 7$
$⟹ x = 1$