Solve (3^{5}*5^-4)*(2^3*3^-7*5^6)

$$( 3 ^ { 5 } \cdot 5 ^ { - 4 } ) \cdot ( 2 ^ { 3 } \cdot 3 ^ { - 7 } \cdot 5 ^ { 6 } )$$

Evaluate

$$\frac{200}{9}\approx 22.222222222$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -7 to get -2.

$$3^{-2}\times 5^{-4}\times 2^{3}\times 5^{6}$$

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$3^{-2}\times 5^{2}\times 2^{3}$$

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

$$\frac{1}{9}\times 5^{2}\times 2^{3}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{1}{9}\times 25\times 2^{3}$$

Multiply \frac{1}{9} and 25 to get \frac{25}{9}.

$$\frac{25}{9}\times 2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{25}{9}\times 8$$

Multiply \frac{25}{9} and 8 to get \frac{200}{9}.

$$\frac{200}{9}$$

Factor

$$\frac{2 ^ {3} \cdot 5 ^ {2}}{3 ^ {2}} = 22\frac{2}{9} = 22.22222222222222$$