Mathematics: Help please and thanks :)

Help please and thanks :) - id7772845, johndemarian310

Shamiyah732

02.02.2022

- $\frac{11}{3}$

Step-by-step explanation:

Using the rules of exponents

$\frac{1}{a^{m} }$ ⇔ $a^{-m}$

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

Consider the right side

$(\frac{1}{27}) ^{a+3}$

= $(\frac{1}{3^3}) ^{a+3}$

= $(3^{-3}) ^{a+3}$

= $3^{(-3a-9)}$

Now we have

9 = $3^{(-3a-9)}$ , that is

3² = $3^{(-3a-9)}$

Since the bases on both sides are equal, equate the exponents

- 3a - 9 = 2 ( add 9 to both sides )

- 3a = 11 ( divide both sides by - 3 )

a = - $\frac{11}{3}$

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