Question

Simplify:

$\left(i\right)0.005\times {10}^2-5\times {10}^{-1}$

$\left(ii\right)\frac{(2^5{)}^2\times 7^3}{8^3\times 7}$

[4 MARKS]

Answer 1

Each question: 2 Marks

i) It's easy to subtract powers when we convert them into normal form.

$0.005\times {10}^2=0.5$ (move the decimal point 2 places to the right)

$5\times {10}^{-1}=0.5$ (move the decimal point 1 place to the left)

Now,

$0.005\times {10}^2-5\times {10}^{-1}$

$=0.5-0.5$

$=0$

ii)
$\frac{(2^5{)}^2\times 7^3}{8^3\times 7}$

= $\frac{(2^5{)}^2\times 7^3}{8^3\times 7}$

= $\frac{\left(2^{5\times 2}\right)\times 7^3}{(2^3{)}^3\times 7}$

= $\frac{2^{10}\times 7^3}{2^9\times 7}$

= $2^{10-9}\times 7^{3-1}=2\times 7^2$

= $2\times 49=98$