Solve frac{9^{4}*3^{2}*3^5-(27)}{(5^2)^5*2^3}=1/27

$$\frac { 9 ^ { 4 } \times 3 ^ { 2 } \times 3 ^ { 5 } - ( 27 ) } { ( 5 ^ { 2 } ) ^ { 5 } \times 2 ^ { 3 } } = \frac { 1 } { 27 }$$

Verify

Solution Steps

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

$$\frac{9^{4}\times 3^{7}-27}{\left(5^{2}\right)^{5}\times 2^{3}}=\frac{1}{27}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{9^{4}\times 3^{7}-27}{5^{10}\times 2^{3}}=\frac{1}{27}$$

Calculate 9 to the power of 4 and get 6561.

$$\frac{6561\times 3^{7}-27}{5^{10}\times 2^{3}}=\frac{1}{27}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{6561\times 2187-27}{5^{10}\times 2^{3}}=\frac{1}{27}$$

Multiply 6561 and 2187 to get 14348907.

$$\frac{14348907-27}{5^{10}\times 2^{3}}=\frac{1}{27}$$

Subtract 27 from 14348907 to get 14348880.

$$\frac{14348880}{5^{10}\times 2^{3}}=\frac{1}{27}$$

Calculate 5 to the power of 10 and get 9765625.

$$\frac{14348880}{9765625\times 2^{3}}=\frac{1}{27}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{14348880}{9765625\times 8}=\frac{1}{27}$$

Multiply 9765625 and 8 to get 78125000.

$$\frac{14348880}{78125000}=\frac{1}{27}$$

Reduce the fraction \frac{14348880}{78125000} to lowest terms by extracting and canceling out 40.

$$\frac{358722}{1953125}=\frac{1}{27}$$

Least common multiple of 1953125 and 27 is 52734375. Convert \frac{358722}{1953125} and \frac{1}{27} to fractions with denominator 52734375.

$$\frac{9685494}{52734375}=\frac{1953125}{52734375}$$

Compare \frac{9685494}{52734375} and \frac{1953125}{52734375}.

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