Solve frac{2^{-3}2^{7}3^{3}3^{4}3^-3}{2^32*3^-13^0}

$$\frac { 2 ^ { - 3 } 2 ^ { 7 } 3 ^ { 3 } 3 ^ { 4 } 3 ^ { - 3 } } { 2 ^ { 3 } 2 \cdot 3 ^ { - 1 } 3 ^ { 0 } }$$

Evaluate

$$243$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 7 to get 4.

$$\frac{2^{4}\times 3^{3}\times 3^{4}\times 3^{-3}}{2^{3}\times 2\times 3^{-1}\times 3^{0}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{2^{4}\times 3^{7}\times 3^{-3}}{2^{3}\times 2\times 3^{-1}\times 3^{0}}$$

To multiply powers of the same base, add their exponents. Add 7 and -3 to get 4.

$$\frac{2^{4}\times 3^{4}}{2^{3}\times 2\times 3^{-1}\times 3^{0}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{2^{4}\times 3^{4}}{2^{4}\times 3^{-1}\times 3^{0}}$$

To multiply powers of the same base, add their exponents. Add -1 and 0 to get -1.

$$\frac{2^{4}\times 3^{4}}{2^{4}\times 3^{-1}}$$

Cancel out 2^{4} in both numerator and denominator.

$$\frac{3^{4}}{\frac{1}{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$3^{5}$$

Calculate 3 to the power of 5 and get 243.

$$243$$

Factor

$$3^{5}$$