Solve {l}{a=-3^{0}+4^{-1}}{B=(3^{-2}+3^-2)^-1}{c=8^-2/2^-1}

$$\left. \begin{array} { l } { a = - 3 ^ { 0 } + 4 ^ { - 1 } } \\ { B = ( 3 ^ { - 2 } + 3 ^ { - 2 } ) ^ { - 1 } } \\ { c = \frac { 8 ^ { - 2 } } { 2 ^ { - 1 } } } \end{array} \right.$$

Solve for a, B, c

$$a=-\frac{3}{4}=-0.75$$

$$B = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$c=\frac{1}{32}=0.03125$$

Solution Steps

Consider the first equation. Calculate 3 to the power of 0 and get 1.

$$a=-1+4^{-1}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$a=-1+\frac{1}{4}$$

Add -1 and \frac{1}{4} to get -\frac{3}{4}.

$$a=-\frac{3}{4}$$

Consider the second equation. Calculate 3 to the power of -2 and get \frac{1}{9}.

$$B=\left(\frac{1}{9}+3^{-2}\right)^{-1}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$B=\left(\frac{1}{9}+\frac{1}{9}\right)^{-1}$$

Add \frac{1}{9} and \frac{1}{9} to get \frac{2}{9}.

$$B=\left(\frac{2}{9}\right)^{-1}$$

Calculate \frac{2}{9} to the power of -1 and get \frac{9}{2}.

$$B=\frac{9}{2}$$

Consider the third equation. Calculate 8 to the power of -2 and get \frac{1}{64}.

$$c=\frac{\frac{1}{64}}{2^{-1}}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$c=\frac{\frac{1}{64}}{\frac{1}{2}}$$

Divide \frac{1}{64} by \frac{1}{2} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{2}.

$$c=\frac{1}{64}\times 2$$

Multiply \frac{1}{64} and 2 to get \frac{1}{32}.

$$c=\frac{1}{32}$$

The system is now solved.

$$a=-\frac{3}{4} B=\frac{9}{2} c=\frac{1}{32}$$