Question

Simplify using laws of exponents:1000×5²×2²÷25×16×10²

Answer 1

Answer= 2.5

Step-by-step explanation:

$\frac{1000 \times 5 {}^{2} \times 2 {}^{2} }{25 \times 16 \times 10 {}^{2} }$

$= \frac{10^3\times 5^2 \times 2^2}{5^{2} \times 4^{2} \times 10 {}^{2} }$

Since,

$4 = 2 {}^{2}$

Thus,

${4}^{2} = {2}^{2 \times 2}$

$= \frac{ {10}^{3} \times {5}^{2} \times {2}^{2} }{ {5}^{2} \times {2}^{2 \times 2} \times {10}^{2} }$

Since,

$a^m/a^n=a^{m - n}$

Therefore,

$10 {}^{3 - 2} \times 5 {}^{2 - 2} \times 2^{2 - 4}$

$= {10 {}^{1} \times {5}^{0} \times 2 {}^{ - 2} }$

Since,

${a}^{0} = 1$

Also,

${a}^{ - m} = \frac{1}{ {a}^{m} }$

Therefore,

$\frac{10 \times 1}{ {2}^{2} }$

$= \frac{10}{4}$

$= 2.5$

Answer 2

꧁SOLUTION꧂

✧♥༻༺♥✧

• At first splitting the terms here
• according to the law of exponents

$↪ \frac{1000 \times {5}^{2} \times {2}^{2} }{25 \times 16 \times {10}^{2} } \\ \\ ↪ \frac{ {10}^{3} \times {5}^{2} \times {2}^{2} }{ {5}^{2} \times {2}^{4} \times {10}^{2} } \\ \\ ↪ \frac{ {5}^{3} \times {2}^{3} \times {5}^{2} \times {2}^{2} }{ {5}^{2} \times {2}^{4} \times {5}^{2} \times {2}^{2} } \\ \\ ↪ \frac{ {5}^{3 - 2} \times {2}^{3 - 2} }{ {5}^{2 - 2} \times {2}^{4 - 2} } \\ \\ ↪ \frac{5 \times 2}{1 \times 4} = \frac{10}{4} = \frac{5}{2}$