Question

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

• A. 1
• B. 2
• C. 3
• D. -1

Answer 1

The correct option is A

1

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

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

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.

$m+6=7$

$⟹m=7–6=1$