Solve (7^{10}div7)^6*(10^5*2^4*2)^3=

$$( 7 ^ { 10 } \div 7 ) ^ { 6 } \cdot ( 10 ^ { 5 } \cdot 2 ^ { 4 } \cdot 2 ) ^ { 3 } =$$

Evaluate

$$141495978144446433330308484225686833972912090284032000000000000000$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 10 to get 9.

$$\left(7^{9}\right)^{6}\times \left(10^{5}\times 2^{4}\times 2\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 6 to get 54.

$$7^{54}\times \left(10^{5}\times 2^{4}\times 2\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$7^{54}\times \left(10^{5}\times 2^{5}\right)^{3}$$

Calculate 7 to the power of 54 and get 4318114567396436564035293097707728087552248849.

$$4318114567396436564035293097707728087552248849\times \left(10^{5}\times 2^{5}\right)^{3}$$

Calculate 10 to the power of 5 and get 100000.

$$4318114567396436564035293097707728087552248849\times \left(100000\times 2^{5}\right)^{3}$$

Calculate 2 to the power of 5 and get 32.

$$4318114567396436564035293097707728087552248849\times \left(100000\times 32\right)^{3}$$

Multiply 100000 and 32 to get 3200000.

$$4318114567396436564035293097707728087552248849\times 3200000^{3}$$

Calculate 3200000 to the power of 3 and get 32768000000000000000.

$$4318114567396436564035293097707728087552248849\times 32768000000000000000$$

Multiply 4318114567396436564035293097707728087552248849 and 32768000000000000000 to get 141495978144446433330308484225686833972912090284032000000000000000.

$$141495978144446433330308484225686833972912090284032000000000000000$$

Factor

$$2^{30}\times 5^{15}\times 7^{54}$$