Question

simplify the question ​

Answer 1

Answer:

do reciprocal

(') means raised to power

25 means 5'2

Step-by-step explanation:

5'6 × 6'4 *5'2/ 3'5 * 10'4

= 5'(6+2) = 5'8

6'4 = 2*3'4 =2'4 * 3'4

10 = 5*2

5'4 * 2'4

given sum becomes

5'8 * 2'4 * 3'4/ 3'5 * 5'4 * 2'4

= there are two 2'4 therefore they would be cut

sum becomes

5'8 * 3'4 / 3'5 * 5'4

thus,

5'(8-4) = 5'4

now,

3'(5-4) = 3'1. or 3

answer is 5'4/3

Answer 2

Given Question :-

$\frac{ {3}^{ - 5} \times {10}^{ - 4} \times 25}{ {5}^{ - 6} \times {6}^{ - 4} }$

As According To The rule of exponents , If the power of any base is -ve . So we have to make it positive .

Solution :-

$\frac{ {5}^{6} \times {6}^{4} \times 25 }{ {3}^{5} \times {10}^{4} }$

$\frac{ {5}^{6} \times ( {2 \times 3)}^{4} \times {5}^{2} }{ {3}^{5} \times {(2 \times 5)}^{4} }$

$\frac{ {5}^{6} \times {2}^{4} \times {3}^{4} \times {5}^{2} }{ {3}^{5} \times {5}^{4} \times {2}^{4} }$

Now we have to use the formula

${a}^{x} \times {a}^{y} = {(a)}^{x + y}$

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

Cancelling 3 , 2 and 5 from Both numerator and Denominator .

$\frac{ {5}^{4} }{3}$

$\frac{625}{3}$

Therefore, answer is 625/3 . If the answer is wrong so kindly use the comment section.