Number Operations and Properties

$ 225 = 25 \times 9$
$ 225 = (5\times 5)  \times (3 \times 3)$

Given, ${ 4 }^{ n-2 }+{ 4 }^{ 2 }=32$
${ 4 }^{ n-2 }=32-{ 4 }^{ 2 }$
${ 4 }^{ n-2 }=32-16$
${ 4 }^{ n-2 }=16$
${ 4 }^{ n-2 }={ 4 }^{ 2 }$
$n-2=2$ ..... (as the bases are equal)
$n=4$

Given, ${7}^{n}$ $\times$ ${7}^{3}$ $=$ ${7}^{12}$

Standard form of $900000000 + 800000 + 50000 + 3000 + 20 + 3 = 90,08,53,023$
$\therefore$ Option C is correct.

Standard form of $900000000 + 3000+7=900003007$

We know that

We need to write it in a standard form:

$8.73\times 10^7=87300000$

On adding, we get

Given Exp. $=-84\times (30-1)+365$
$=-(84\times 30)+84+365$
$=-2520+449$
$=-2071$

Given Exp. $=\cfrac { 800 }{ 64 } \times \cfrac { 1296 }{ 36 } =450$

$58+\cfrac{3}{100}+\cfrac{7}{1000}$
$=58+\cfrac{0}{10}+\cfrac{3}{100}+\cfrac{7}{1000}=58.037$

Let the required number be $x$
According to question, we have
$0.75$ of $x$ $=1200$
$\Rightarrow \displaystyle\frac{75}{100}\times x=1200$
$\Rightarrow \displaystyle x=1200\times \frac{100}{75}=1600$
Therefore, required number is $1600$.
Now, $\displaystyle\frac{5}{8}$ of the number $=\displaystyle\frac{5}{8}\times 1600=1000$.

Value=$540\times \dfrac{2}{3}=360$

$60\% \ of \ 264 =\dfrac{60}{100} \times 264 =158.4$