Question

Question 1
Simplify :
(i) (2⁵ × 7³) ÷ (8³ × 7) (ii) (25 × 5² × t⁸) ÷ (10³ × t⁴)

Answer 1

Given:-

1. $( {2}^{5} \times {7}^{3} ) \div ( {8}^{3} \times 7)$
2. $(25 \times {5}^{2} \times {t}^{8}) \div ( {10}^{3 } \times {t}^{4} )$

To find

• simplyfy

Solution:-

$( {2}^{5} \times {7}^{3} ) \div ( {8}^{3} \times 7) \\ \\ open \: this \: as \: much \: as \: u \: want \\ \\ \frac{2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7}{8 \times 8 \times 8 \times \times 7} \\ \\ \frac{ {7}^{2} }{ {4}^{2} } \\ \\ {(\frac{7}{4} )}^{2} \\ \\ \frac{49}{16}$

for 2 nd que:-

$(25 \times {5}^{2} \times {t}^{8}) \div ( {10}^{3 } \times {t}^{4} ) \\ \\ \frac{25 \times 5 \times 5 \times t \times t \times t \times t \times t \times t \times t \times t}{10 \times 10 \times 10 \times t \times t \times t \times t} \\ \\ \frac{5 \times {t}^{4} }{ {2}^{3} } \\ \\ \frac{5 \times {t}^{4} }{8}$

Answer 2

$(2^5\times 7^3)\div(8^3\times 7)$ $=3\frac{1}{16}$

$(25 \times 5^2 \times t^8)\div(10^3\times t^4)$ $=\frac{5t^4}{8}$

Step-by-step explanation:

(i)$(2^5\times 7^3)\div(8^3\times 7)$

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

$=\frac{2^5\times 7^3}{2^9\times 7}$

$=2^{(5-9)}\times 7^{(3-1)$

$=\frac{7^2}{2^4}$

$=\frac{49}{16}$

$=3\frac{1}{16}$

(ii)$(25 \times 5^2 \times t^8)\div(10^3\times t^4)$

$=\frac{5^4\times t^8}{5^3\times 2^3\times t^4}$

$=\frac{5^{4-3} \times t^{(8-4)}}{2^3}$

$=\frac{5t^4}{8}$