Question

A space rocket can carry $6^5\times 4^5$ lb of small satellite rockets with it. Each small satellite weighs $4^7$ lb.
How many small satellite rockets can be carried by the space rocket?

• A. 486

Answer 1

The correct option is A 486
A space rocket can carry $6^5\times 4^5\mathrm{lb}$ of small satellite.
You know, $a^x\times b^x={(a\times b)}^x=a{b}^x$
So, the space rocket carries = $6^5\times 4^5={(6\times 4)}^5={24}^5$ lb of small satellite rockets.
Now, weight of each small satellite rocket = $4^7\mathrm{lb}.$
∴ The number of small satellite rockets will be
$\frac{{24}^5}{4^7}=\frac{4^5\times 6^5}{4^7}=6^5\times 4^{(5-7)}[\because a^x÷a^y=a^{x-y}]=6^5\times 4^{-2}=\frac{6\times 6\times 6\times 6\times 6}{4^2}=\frac{6\times 6\times 6\times 6\times 6}{4\times 4}=3\times 3\times 3\times 3\times 6=9\times 9\times 6=81\times 6=486$
So, 486 small rocket satellites can be carried by the space rocket.