Solve (3^{2})^{5}*(3^{2}x^{2}-4^{2})^3*(11^7)^2*2^4

$$( 3 ^ { 2 } ) ^ { 5 } \times ( 3 ^ { 2 } x ^ { 2 } - 4 ^ { 2 } ) ^ { 3 } \times ( 11 ^ { 7 } ) ^ { 2 } \times 2 ^ { 4 }$$

Evaluate

$$358781566772108764944\left(9x^{2}-16\right)^{3}$$

Solution Steps

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

$$3^{10}\left(3^{2}x^{2}-4^{2}\right)^{3}\times \left(11^{7}\right)^{2}\times 2^{4}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$3^{10}\left(3^{2}x^{2}-4^{2}\right)^{3}\times 11^{14}\times 2^{4}$$

Calculate 3 to the power of 10 and get 59049.

$$59049\left(3^{2}x^{2}-4^{2}\right)^{3}\times 11^{14}\times 2^{4}$$

Calculate 3 to the power of 2 and get 9.

$$59049\left(9x^{2}-4^{2}\right)^{3}\times 11^{14}\times 2^{4}$$

Calculate 4 to the power of 2 and get 16.

$$59049\left(9x^{2}-16\right)^{3}\times 11^{14}\times 2^{4}$$

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(9x^{2}-16\right)^{3}.

$$59049\left(729\left(x^{2}\right)^{3}-3888\left(x^{2}\right)^{2}+6912x^{2}-4096\right)\times 11^{14}\times 2^{4}$$

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

$$59049\left(729x^{6}-3888\left(x^{2}\right)^{2}+6912x^{2}-4096\right)\times 11^{14}\times 2^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$59049\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 11^{14}\times 2^{4}$$

Calculate 11 to the power of 14 and get 379749833583241.

$$59049\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 379749833583241\times 2^{4}$$

Multiply 59049 and 379749833583241 to get 22423847923256797809.

$$22423847923256797809\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$22423847923256797809\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 16$$

Multiply 22423847923256797809 and 16 to get 358781566772108764944.

$$358781566772108764944\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)$$

Use the distributive property to multiply 358781566772108764944 by 729x^{6}-3888x^{4}+6912x^{2}-4096.

$$261551762176867289644176x^{6}-1394942731609958878102272x^{4}+2479898189528815783292928x^{2}-1469569297498557501210624$$

Expand

$$261551762176867289644176x^{6}-1394942731609958878102272x^{4}+2479898189528815783292928x^{2}-1469569297498557501210624$$

Solution Steps

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

$$3^{10}\left(3^{2}x^{2}-4^{2}\right)^{3}\times \left(11^{7}\right)^{2}\times 2^{4}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$3^{10}\left(3^{2}x^{2}-4^{2}\right)^{3}\times 11^{14}\times 2^{4}$$

Calculate 3 to the power of 10 and get 59049.

$$59049\left(3^{2}x^{2}-4^{2}\right)^{3}\times 11^{14}\times 2^{4}$$

Calculate 3 to the power of 2 and get 9.

$$59049\left(9x^{2}-4^{2}\right)^{3}\times 11^{14}\times 2^{4}$$

Calculate 4 to the power of 2 and get 16.

$$59049\left(9x^{2}-16\right)^{3}\times 11^{14}\times 2^{4}$$

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(9x^{2}-16\right)^{3}.

$$59049\left(729\left(x^{2}\right)^{3}-3888\left(x^{2}\right)^{2}+6912x^{2}-4096\right)\times 11^{14}\times 2^{4}$$

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

$$59049\left(729x^{6}-3888\left(x^{2}\right)^{2}+6912x^{2}-4096\right)\times 11^{14}\times 2^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$59049\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 11^{14}\times 2^{4}$$

Calculate 11 to the power of 14 and get 379749833583241.

$$59049\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 379749833583241\times 2^{4}$$

Multiply 59049 and 379749833583241 to get 22423847923256797809.

$$22423847923256797809\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$22423847923256797809\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)\times 16$$

Multiply 22423847923256797809 and 16 to get 358781566772108764944.

$$358781566772108764944\left(729x^{6}-3888x^{4}+6912x^{2}-4096\right)$$

Use the distributive property to multiply 358781566772108764944 by 729x^{6}-3888x^{4}+6912x^{2}-4096.

$$261551762176867289644176x^{6}-1394942731609958878102272x^{4}+2479898189528815783292928x^{2}-1469569297498557501210624$$