Question

I am once again in need of mathematical guidance

Answer 1

Answer:

a=-3

b=5/2

c=-1/2

Step-by-step explanation:

3^-3=1/3^3=1/27    a=-3

3^5/2=√3^5=9√3           b=5/2

3^-1/2=1/√3                         c=-1/2

Answer 2

Answer:

1. a = -3
2. b = 5/2
3. c = -1/2

Step-by-step explanation:

$3^a = 1/27\\Write ; 1/27 -in-exponential-form\\3^a = 3^-^3\\Cancel-out-the-base\\a = -3$

$3^b = 9\sqrt{3} \\Convert 9\sqrt{3} to base 3\\ 3^b = 3^{\frac{5}{2} } \\Cancel-out-the-base\\b = 5/2$

$3^c = \frac{1}{\sqrt{3} } \\Apply -exponent -rule ;\frac{1}{a^b}=a^{-b}\\\frac{1}{\sqrt{3}}=3^{-\frac{1}{2}}\\3^c = 3^{-\frac{1}{2} } \\\mathrm{Apply\:exponent\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\\3^{-\frac{1}{2}}=3^{-\frac{1}{2}}\\3^c = 3^{-\frac{1}{2} } \\\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)\\c = -\frac{1}{2}$

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