Solve [1/4]^-2-3(8)^3*4^0+[9/16]^-frac{1{2}}

$$[ \frac { 1 } { 4 } ] ^ { - 2 } - 3 ( 8 ) ^ { 3 } \times 4 ^ { 0 } + [ \frac { 9 } { 16 } ] ^ { - \frac { 1 } { 2 } }$$

Evaluate

$$-\frac{4556}{3}\approx -1518.666666667$$

Solution Steps

Calculate \frac{1}{4} to the power of -2 and get 16.

$$16-3\times 8^{3}\times 4^{0}+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$$

Calculate 8 to the power of 3 and get 512.

$$16-3\times 512\times 4^{0}+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$$

Multiply 3 and 512 to get 1536.

$$16-1536\times 4^{0}+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$$

Calculate 4 to the power of 0 and get 1.

$$16-1536\times 1+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$$

Multiply 1536 and 1 to get 1536.

$$16-1536+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$$

Subtract 1536 from 16 to get -1520.

$$-1520+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$$

Calculate \frac{9}{16} to the power of -\frac{1}{2} and get \frac{4}{3}.

$$-1520+\frac{4}{3}$$

Add -1520 and \frac{4}{3} to get -\frac{4556}{3}.

$$-\frac{4556}{3}$$

Factor

$$-\frac{4556}{3} = -1518\frac{2}{3} = -1518.6666666666667$$