Solve 2(2^{2}*2^-3*2^-1*3^2)^2

$$2 ( 2 ^ { 2 } \cdot 2 ^ { - 3 } \cdot 2 ^ { - 1 } \cdot 3 ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{81}{8}=10.125$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$2\times \left(2^{-1}\times 2^{-1}\times 3^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add -1 and -1 to get -2.

$$2\times \left(2^{-2}\times 3^{2}\right)^{2}$$

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

$$2\times \left(\frac{1}{4}\times 3^{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$2\times \left(\frac{1}{4}\times 9\right)^{2}$$

Multiply \frac{1}{4} and 9 to get \frac{9}{4}.

$$2\times \left(\frac{9}{4}\right)^{2}$$

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$2\times \frac{81}{16}$$

Multiply 2 and \frac{81}{16} to get \frac{81}{8}.

$$\frac{81}{8}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {3}} = 10\frac{1}{8} = 10.125$$