Solve {[(9^{2})^{3}]^{5}:(9^{8})^{3}}^{2}*{[(3^{5})^{7}]^{2}*(3^{6})^{3}:[(3^{19})^{2}]^2}:[(2+5^2)^6]^2

$$\{ [ ( 9 ^ { 2 } ) ^ { 3 } ] ^ { 5 } : ( 9 ^ { 8 } ) ^ { 3 } \} ^ { 2 } \cdot \{ [ ( 3 ^ { 5 } ) ^ { 7 } ] ^ { 2 } \cdot ( 3 ^ { 6 } ) ^ { 3 } : [ ( 3 ^ { 19 } ) ^ { 2 } ] ^ { 2 } \} : [ ( 2 + 5 ^ { 2 } ) ^ { 6 } ] ^ { 2 }$$

Evaluate

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Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(\frac{\left(9^{6}\right)^{5}}{\left(9^{8}\right)^{3}}\right)^{2}\times \frac{\left(\left(3^{5}\right)^{7}\right)^{2}\times \left(3^{6}\right)^{3}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$\frac{\left(\frac{9^{30}}{\left(9^{8}\right)^{3}}\right)^{2}\times \frac{\left(\left(3^{5}\right)^{7}\right)^{2}\times \left(3^{6}\right)^{3}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{\left(\frac{9^{30}}{9^{24}}\right)^{2}\times \frac{\left(\left(3^{5}\right)^{7}\right)^{2}\times \left(3^{6}\right)^{3}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 24 from 30 to get 6.

$$\frac{\left(9^{6}\right)^{2}\times \frac{\left(\left(3^{5}\right)^{7}\right)^{2}\times \left(3^{6}\right)^{3}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{9^{12}\times \frac{\left(\left(3^{5}\right)^{7}\right)^{2}\times \left(3^{6}\right)^{3}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 7 to get 35.

$$\frac{9^{12}\times \frac{\left(3^{35}\right)^{2}\times \left(3^{6}\right)^{3}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 35 and 2 to get 70.

$$\frac{9^{12}\times \frac{3^{70}\times \left(3^{6}\right)^{3}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{9^{12}\times \frac{3^{70}\times 3^{18}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 70 and 18 to get 88.

$$\frac{9^{12}\times \frac{3^{88}}{\left(\left(3^{19}\right)^{2}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 19 and 2 to get 38.

$$\frac{9^{12}\times \frac{3^{88}}{\left(3^{38}\right)^{2}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 38 and 2 to get 76.

$$\frac{9^{12}\times \frac{3^{88}}{3^{76}}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 76 from 88 to get 12.

$$\frac{9^{12}\times 3^{12}}{\left(\left(2+5^{2}\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{9^{12}\times 3^{12}}{\left(2+5^{2}\right)^{12}}$$

Calculate 9 to the power of 12 and get 282429536481.

$$\frac{282429536481\times 3^{12}}{\left(2+5^{2}\right)^{12}}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{282429536481\times 531441}{\left(2+5^{2}\right)^{12}}$$

Multiply 282429536481 and 531441 to get 150094635296999121.

$$\frac{150094635296999121}{\left(2+5^{2}\right)^{12}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{150094635296999121}{\left(2+25\right)^{12}}$$

Add 2 and 25 to get 27.

$$\frac{150094635296999121}{27^{12}}$$

Calculate 27 to the power of 12 and get 150094635296999121.

$$\frac{150094635296999121}{150094635296999121}$$

Divide 150094635296999121 by 150094635296999121 to get 1.

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Factor

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