Question

Find the value of m​

Answer 1

Answer:

m = 9

Step-by-step explanation:

Using the rules of exponents

$(a^m)^{n}$ = $a^{mn}$

$a^{m}$ × $a^{n}$ ⇔ $a^{(m+n)}$

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

Then

$(\frac{1}{27}) ^{m}$ × $(81)^{-1}$ = 243 ← express all values to base 3

$(\frac{1}{3^3}) ^{m}$ × $(3 ^4)^{-1}$ = $3^{5}$

$(3^-3)^{m}$ × $3^{-4}$ = $3^{5}$

$3^{-3m}$ × $3^{-4}$ = $3^{5}$

$3^{(-3m-4)}$ = $3^{5}$

Since bases on both sides are equal, both 3 , then equate exponents

- 3m - 4 = 5 ( add 4 to both sides )

- 3m = 9 ( divide both sides by - 3 )

m = - 3