Question
Simplify and express each of the following in exponential form.
$25^4÷5^3$
$25^4÷5^3$
✓
Answer
We have,
$25^4 \div 5^3=\left(5^2\right)^4÷5^3$ $\left[\because 25=5 \times 5=5^2\right]$
$=5^{2 \times 4} \div 5^3=5^8 \div 5^3$ $\left[\because\left(a^m\right)^n=a^{m n}\right]$
$=5^{8-3}=5^5$ $\left[\because a^m \div a^n=a^{m-n}\right]$
$25^4 \div 5^3=\left(5^2\right)^4÷5^3$ $\left[\because 25=5 \times 5=5^2\right]$
$=5^{2 \times 4} \div 5^3=5^8 \div 5^3$ $\left[\because\left(a^m\right)^n=a^{m n}\right]$
$=5^{8-3}=5^5$ $\left[\because a^m \div a^n=a^{m-n}\right]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.
Find the area enclosed by the following figure:
Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?
Draw an isosceles triangle in which each of the equal sides is of length $3\ cm$ and the angle between them is $45^\circ $.
→Construct an obtuse angled triangle which has a base of $5.5\ cm$ and base angles of $30^\circ $ and $120^\circ .$
→From, $x^3-5 x^2+3 x+1$, take away $6 x^2-4 x^3+5+3 x$
→$DL$ and $BM$ are the heights on sides $AB$ and $AD$ respectively of parallelogram $ABCD.$ If the area of the parallelogram is $1470 \mathrm{~cm}^2$ and $AB = 35\ cm$ and $AD = 49\ cm$, Find the length of $BM$ and $DL.$
→Simplify the following algebraic expressions by removing grouping symbols: $3x + 2y - [x - (2y - 3)]$
→Add the following rational numbers: $\frac{31}{-4}\text{ and }\frac{-5}{8}$
→What number must be subtracted from each of the numbers $10, 12, 19, 24$ to get the numbers which are in proportion$?$
→