Question

Find the value of x in the following: ​

Answer 1

Step-by-step explanation:

Question :

(b)

$( \frac{2}{5} ) {}^{ - 4} \div ( \frac{2}{5} ) {}^{ - 8} = ( \frac{2}{5} ) {}^{2x}$

Solution :

$( \frac{2}{5} ) {}^{ - 4 - ( - 8)} = ( \frac{2}{5} ) {}^{2x}$

$( \frac{2}{5} ) {}^{ - 4 + 8} = ( \frac{2}{5} ) {}^{2x}$

$4 = 2x$

$\frac{4}{2} = x$

$2 = x$

: Value of x is 2.

(c)

${5}^{x} \times {5}^{ - 8} = {5}^{ - 3}$

Solution :

$5 {}^{x} = \frac{ {5}^{ - 3} }{ {5}^{ - 8} }$

${5}^{x} = {5}^{ - 3 - ( - 8)}$

${5}^{x} = {5}^{ - 3 + 8}$

${5}^{x} = {5}^{5}$

$x = 5$

: Value of x is 5.

(c)

${6}^{0} \div {6}^{ - 1} = {6}^{x}$

Solution :

${6}^{0 - ( - 1)} = {6}^{x}$

${6}^{1} = {6}^{x}$

$1 = x$

: Value of x is 1.

More information :

1. In the class if multiplicationwe add the powers when the bases are same and powers are different.

Example :

$= > {5}^{2} \times {5}^{9}$

$= > {5}^{(2 + 9)}$

$= > {5}^{11} \: \: ans..$

2. In the case if division we subtract the powers when the bases are same.

Example :

$= > {3}^{6} \div {3}^{4}$

$= > {3}^{(6 - 4)}$

$= > {3}^{2} \: \: ans..$

3. When the powers are same and the bases are different we multiply the bases.

Example :

$= > {5}^{6} \times {2}^{6}$

$= > (5 \times 2) {}^{6}$

$= > {10}^{6}$

4. When there are 2 powers one inside the bracket and one outside we multiply them.

Example :

$= ({5}^{2} ) {}^{3}$

$= > {5}^{3 \times 2}$

$= > {5}^{6} \: \: ans..$

5. Anything raise to power 0 is 1.

Example :

$= > {10}^{0}$

$= > 1$

6. Anything raise to power negetive, then the number become reciprocal.

For example :

$= > 3 {}^{ - 1}$

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

Hope it helps you!!!

Thank you!!