Find the value of m if -10 m -1-105-107-A- -1B- 1C- 2D- 3

The correct option is B 1 Consider the equation ( 10)^m+1× ( 10)^5 nbsp;= ( 10)^7. ( 10)^m+1+5 nbsp;= ( 10)^7 (∵ a^m× a^n=a^m+n) i.e., ( 10)^m+6 nbsp;= ...

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Byju's Answer

Standard VIII

Mathematics

Laws of Exponents

Find the valu...

Question

Find the value of $m$ if $(- 10)^{m + 1} \times (- 10)^{5} = (- 10)^{7} .$

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Solution

The correct option is A
1

Consider the equation $(- 10)^{m + 1} \times (- 10)^{5} = (- 10)^{7} .$

$(- 10)^{m + 1 + 5} = (- 10)^{7} (∵ a^{m} \times a^{n} = a^{m + n})$

i.e., $(- 10)^{m + 6} = (- 10)^{7}$

Powers on both the sides of the equation have the same base. So, their exponents must also be equal.

$m + 6 = 7$

$⟹ m = 7 - 6 = 1$

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Find the value of m if (−10)m+1×(−10)5=(−10)7.

The correct option is A 1 Consider the equation (−10)m+1×(−10)5=(−10)7. (−10)m+1+5=(−10)7 (∵am×an=am+n) i.e., (−10)m+6=(−10)7 Powers on both the sides of the equation have the same base. So, their exponents must also be equal. m+6=7 ⟹m=7–6=1

Find the value of $m$ if $(- 10)^{m + 1} \times (- 10)^{5} = (- 10)^{7} .$