Question

kindly solve this maths question
I need help​

Answer 1

Answer:

1.

$\frac{2}{25}$

2.

$\frac{1}{ - 486}$

3. -2

4. 3

5. 2

Step-by-step explanation:

For the questions

Let the required numbers be x

1. A/q

$x \: \times {- 4}^{ - 2 \: } = {10}^{? - 2}$

$\frac{x}{ { - 4}^{2} } \: = \: \frac{1}{ {10}^{2} }$

$\frac{x}{16} = \frac{1}{100}$

$x \: = \frac{16}{100}$

$x \: = \: \frac{2}{25}$

Ans

2. A/q

$x \: \div ( {\frac{ - 2}{3} )}^{ - 1} \: = {27}^{ - 2}$

$x \: \times \frac{ - 2}{3} \: = \: \frac{1}{{27}^{2} }$

$x \: = \: \frac{3}{ - 2 \times {3}^{6} }$

$x \: = \: \frac{1}{ - 2 \times {3}^{5} }$

$x \: = \: \frac{1}{- 486}$

Ans

3. A/q

$({ \frac{2}{9}) }^{3} \: \times \: ({ \frac{2}{9}) }^{ - 6} \: = \: ({ \frac{2}{9}) }^{2m + 1}$

Since the bases of the exponent are same.

Therefore,

$3 + ( - 6) = 2m + 1$

$3 - 6 = 2m + 1$

$- 3 - 1 = 2m$

$m = \frac{ - 4}{2}$

$m \: = - 2$

Ans.

4. A/q

${5}^{x - 1} \div 25 = 125$

$\frac{ {5}^{2x - 1} }{ {5}^{2} } = {5}^{3}$ Since the bases are same.

Therefore,

$2x - 1 - 2 = 3$

$2x - 3 = 3$

$2x = 6$

$x = 3$

Ans

5. A/q

$\frac{ {2}^{3x - 1} + 10 } { 7} = 6$

${2}^{3x - 1} + 10 = 42$

${2}^{3x - 1} = 32$

${2}^{3x - 1} = 32$

${2}^{3x - 1} = {2}^{5}$

Since the bases are same.

Therefore,

$3x - 1 = 5$

$3x \: = 6$

$x \: = \: 3$

Ans