IMAT 2016 Q60 [Scientific Notation]

x = 3 × 10^m and y = 5 × 10^n where m and n are integers.

Which of the following is an expression, in scientific notation, for xy?

A. 8 × 10 ^{m+n}
B. 1.5 × 10 ^{mn}
C. 15 × 10 ^{m+n­-1}
D. 1.5 × 10^ {mn+1}
E. 1.5 × 10 ^{m+n+1}

It’s important to know: a^c \cdot a^d = a^{c+d}

Using that, we will easily solve this question:

x\cdot y = 3\cdot 10^m \cdot 5 \cdot 10^n = 15 \cdot 10^{m+n} = 1.5 \cdot 10^1\cdot 10^{m+n} = 1.5 \cdot 10^{m+n+1}

So the correct answer to this question, as proved above, is (E)