Question

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

• A. -1
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B

1

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

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

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

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

$\Rightarrow$ m + 6 = 7

$\Rightarrow$ m = 7 – 6 = 1