Question

Question 158(ii)

Find a single machine that will do the same job as the given hook-up.
$a(\times 2^4)$ machine followed by $(\times {\left(\frac{1}{2}\right)}^2)$ 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

$(\times 2^4)$ machine followed by $(\times {\left(\frac{1}{2}\right)}^2)$ machine.
So, it produces $2\times 2\times 2\times 2\times \frac{1}{2}\times \frac{1}{2}=4$
Hence,$\times 2^2$ single machine can do the same job as the given hook-up.