Question

find the value of m ​

Answer 1

Answer:

$( \frac{2}{3}) ^{2 + 5}$

(2/3)⁷=(2/3)^m

by comparison

m=7

(3/7)^(⁴+⁵)

(3/7)^9=(3/7)^2m+1

by comparison

2m+1=9

2m=9-1

2m=8

m=8/2

m=4

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Answer 2

Step-by-step-Explaination :-

$\bf \: 6)i.) \: { \huge(} \dfrac{2}{3} {\huge)} ^{2} \times {\huge(} \dfrac{2}{3}{ \huge)}^{5} = {\huge(} \dfrac{2}{3} {\huge)}^{m}$

Now , we need to know a property of Exponents that is :-

$\rm \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

Here, a is the fraction whereas m and n are the powers of them.

So, it says that value of M will be m+n

$\bf \rightarrow\: { \huge(} \dfrac{2}{3} {\huge)} ^{2} \times {\huge(} \dfrac{2}{3}{ \huge)}^{5} = {\huge(} \dfrac{2}{3} {\huge)}^{2 + 5}$

$\bf \rightarrow\: { \huge(} \dfrac{2}{3} {\huge)} ^{2} \times {\huge(} \dfrac{2}{3}{ \huge)}^{5} = {\huge(} \dfrac{2}{3} {\huge)}^{7}$

$\bf \rightarrow\: { \huge(} \dfrac{2}{3} {\huge)} ^{2} \times {\huge(} \dfrac{2}{3}{ \huge)}^{5} = {\huge(} \dfrac{2}{3} {\huge)}^{7}$$\rm{ \huge \therefore} \: value \: of \: {\bf \: m }\: is \: \bf \: 7$

Since, bases are equal powers are also equal.

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$\bf \: 6)iii.) \: { \huge(} \dfrac{3}{7} {\huge)} ^{4} \times {\huge(} \dfrac{3}{7}{ \huge)}^{5} = {\huge(} \dfrac{3}{7} {\huge)}^{2m + 1}$

Here, same property we have to use

$\rm \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

Since, bases are equal powers are also equal

$\longmapsto\: \rm \bf\: 2m + 1 = 4 + 5$

$\longmapsto \bf \: 2m + 1 = 9$

Positive 1 will go to right side of equal to sign so, it will become negative as it will go to equal to sign.

$\longmapsto \bf \: 2m = 9 - 1$

$\longmapsto \bf \: 2m = 8$

$\longmapsto \bf \: m = \cancel \dfrac{8}{2}$

$\longmapsto \bf \: m = 4$

$\rm{ \huge \therefore} \: value \: of \: {\bf \: m} \: is \: \bf4$