Solve T:(2/3)^-2*3^-1+(pi-2109)^0div(1/4)^-1

$$T : ( \frac { 2 } { 3 } ) ^ { - 2 } \times 3 ^ { - 1 } + ( \pi - 2109 ) ^ { 0 } \div ( \frac { 1 } { 4 } ) ^ { - 1 }$$

Evaluate

$$\frac{4T}{27}+\frac{1}{4}$$

Short Solution Steps

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

$$\frac{T}{\frac{9}{4}}\times 3^{-1}+\frac{\left(\pi -2109\right)^{0}}{\left(\frac{1}{4}\right)^{-1}}$$

Divide T by \frac{9}{4} by multiplying T by the reciprocal of \frac{9}{4}.

$$\frac{T\times 4}{9}\times 3^{-1}+\frac{\left(\pi -2109\right)^{0}}{\left(\frac{1}{4}\right)^{-1}}$$

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

$$\frac{T\times 4}{9}\times \frac{1}{3}+\frac{\left(\pi -2109\right)^{0}}{\left(\frac{1}{4}\right)^{-1}}$$

Multiply \frac{T\times 4}{9} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{T\times 4}{9\times 3}+\frac{\left(\pi -2109\right)^{0}}{\left(\frac{1}{4}\right)^{-1}}$$

Calculate \pi -2109 to the power of 0 and get 1.

$$\frac{T\times 4}{9\times 3}+\frac{1}{\left(\frac{1}{4}\right)^{-1}}$$

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

$$\frac{T\times 4}{9\times 3}+\frac{1}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9\times 3 and 4 is 108. Multiply \frac{T\times 4}{9\times 3} times \frac{4}{4}. Multiply \frac{1}{4} times \frac{27}{27}.

$$\frac{4T\times 4}{108}+\frac{27}{108}$$

Since \frac{4T\times 4}{108} and \frac{27}{108} have the same denominator, add them by adding their numerators.

$$\frac{4T\times 4+27}{108}$$

Do the multiplications in 4T\times 4+27.

$$\frac{16T+27}{108}$$

Factor

$$\frac{16T+27}{108}$$