Solve left(2*5right)^4-left(5*2right)^3+(5^2*5)-5^7/{5^6}+({4}^2*{4}^3*4)-5*{10}^2

$${ \left(2 \times 5 \right) }^{ 4 } - { \left(5 \cdot 2 \right) }^{ 3 } +( { 5 }^{ 2 } \times 5)- \frac{ { 5 }^{ 7 } }{ { 5 }^{ 6 } } +( { 4 }^{ 2 } \times { 4 }^{ 3 } \times 4)-5 \times { 10 }^{ 2 }$$

Evaluate

$$12716$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 7 to get 1.

$$\left(2\times 5\right)^{4}-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{2}\times 4^{3}\times 4-5\times 10^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(2\times 5\right)^{4}-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{5}\times 4-5\times 10^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\left(2\times 5\right)^{4}-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{6}-5\times 10^{2}$$

Multiply 2 and 5 to get 10.

$$10^{4}-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{6}-5\times 10^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$10000-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{6}-5\times 10^{2}$$

Multiply 5 and 2 to get 10.

$$10000-10^{3}+5^{3}-5^{1}+4^{6}-5\times 10^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$10000-1000+5^{3}-5^{1}+4^{6}-5\times 10^{2}$$

Subtract 1000 from 10000 to get 9000.

$$9000+5^{3}-5^{1}+4^{6}-5\times 10^{2}$$

Calculate 5 to the power of 3 and get 125.

$$9000+125-5^{1}+4^{6}-5\times 10^{2}$$

Add 9000 and 125 to get 9125.

$$9125-5^{1}+4^{6}-5\times 10^{2}$$

Calculate 5 to the power of 1 and get 5.

$$9125-5+4^{6}-5\times 10^{2}$$

Subtract 5 from 9125 to get 9120.

$$9120+4^{6}-5\times 10^{2}$$

Calculate 4 to the power of 6 and get 4096.

$$9120+4096-5\times 10^{2}$$

Add 9120 and 4096 to get 13216.

$$13216-5\times 10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$13216-5\times 100$$

Multiply 5 and 100 to get 500.

$$13216-500$$

Subtract 500 from 13216 to get 12716.

$$12716$$

Factor

$$2^{2}\times 11\times 17^{2}$$