Solve 2.5^4-left(5*2right)^3+(5^2*5)-5^7/{5^6}+({4}^2*{4}^34)-5*10

$${ 2.5 }^{ 4 } - { \left(5 \cdot 2 \right) }^{ 3 } +( { 5 }^{ 2 } \times 5)- \frac{ { 5 }^{ 7 } }{ { 5 }^{ 6 } } +( { 4 }^{ 2 } \times { 4 }^{ 3 } 4)-5 \times 10$$

Evaluate

$$3205.0625$$

Solution Steps

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

$$2.5^{4}-\left(5\times 2\right)^{3}+5^{3}-\frac{5^{7}}{5^{6}}+4^{2}\times 4^{3}\times 4-5\times 10$$

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

$$2.5^{4}-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{2}\times 4^{3}\times 4-5\times 10$$

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

$$2.5^{4}-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{5}\times 4-5\times 10$$

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

$$2.5^{4}-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{6}-5\times 10$$

Calculate 2.5 to the power of 4 and get 39.0625.

$$39.0625-\left(5\times 2\right)^{3}+5^{3}-5^{1}+4^{6}-5\times 10$$

Multiply 5 and 2 to get 10.

$$39.0625-10^{3}+5^{3}-5^{1}+4^{6}-5\times 10$$

Calculate 10 to the power of 3 and get 1000.

$$39.0625-1000+5^{3}-5^{1}+4^{6}-5\times 10$$

Subtract 1000 from 39.0625 to get -960.9375.

$$-960.9375+5^{3}-5^{1}+4^{6}-5\times 10$$

Calculate 5 to the power of 3 and get 125.

$$-960.9375+125-5^{1}+4^{6}-5\times 10$$

Add -960.9375 and 125 to get -835.9375.

$$-835.9375-5^{1}+4^{6}-5\times 10$$

Calculate 5 to the power of 1 and get 5.

$$-835.9375-5+4^{6}-5\times 10$$

Subtract 5 from -835.9375 to get -840.9375.

$$-840.9375+4^{6}-5\times 10$$

Calculate 4 to the power of 6 and get 4096.

$$-840.9375+4096-5\times 10$$

Add -840.9375 and 4096 to get 3255.0625.

$$3255.0625-5\times 10$$

Multiply 5 and 10 to get 50.

$$3255.0625-50$$

Subtract 50 from 3255.0625 to get 3205.0625.

$$3205.0625$$

Factor

$$\frac{19 \cdot 2699}{2 ^ {4}} = 3205\frac{1}{16} = 3205.0625$$