Question

Question 158(iii)

Find a single machine that will do the same job as the given hook-up.
$a(\times 5^{99})$ machine followed by a $\left(5^{-100}\right)$ machine.
Maya multiplied $(4^2\times 3^2)$ by thinking about stretching machines.

Use Maya's idea to multiply $5^3\times 2^3$.
Maya's idea is another product law of exponents.
Multiplying Expressions with the same Exponents
$a^c\times b^c=(a\times b{)}^c$
You can use this law with more than two expressions. If the exponents are the same, multiply the expressions by multiplying the bases and using the same exponent. e.g. $2^8\times 3^8\times 7^8=(2\times 3\times 7{)}^8={42}^8$.

Answer 1

$(\times 5^{99})$ machine followed by $\times 5^{-100}$ machine. So, it produces = $5^{99}\times \frac{1}{5^{1}00}=\frac{1}{5}$
Hence, $(\times \frac{1}{5})$ machine can do the same job as the given hook-up.