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

The correct option is D 1 ( 10)^m+1× ( 10)^5 = ( 10)^7 ⇒ ( 10)^m+1+5 = ( 10)^7 nbsp; nbsp; [∵ a^m × a^n = a^(m+n)] ⇒ ( 10)^m+6 = ( 10)^7 Since their bases ...

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Standard IX

Mathematics

Product Law

Find the valu...

Question

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

-1

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Solution

The correct option is C
1

$(- 10)^{m + 1}$ × $(- 10)^{5}$ = $(- 10)^{7}$

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

$\Rightarrow (- 10)^{m + 6}$ = $(- 10)^{7}$

Since their bases are equal, their exponents must be equal.

$\Rightarrow$ m + 6 = 7

$\Rightarrow$ 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 C 1 (−10)m+1× (−10)5 = (−10)7 ⇒(−10)m+1+5 = (−10)7 [∵am×an = a(m+n)] ⇒(−10)m+6 = (−10)7 Since their bases are equal, their exponents must be equal. ⇒ m + 6 = 7 ⇒ m = 7 – 6 = 1

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