Solve 5^25^35^7/5^4{5^{5}5}-{left(frac{1/2right)}^{4}{left(1/2right)}^{3}{left(1/2right)}^2}{{left(frac{1}{2}right)}^5{left(frac{1}{2}right)}^2{left(frac{1}{2}right)}^2}

$$\frac{ { 5 }^{ 2 } { 5 }^{ 3 } { 5 }^{ 7 } }{ { 5 }^{ 4 } { 5 }^{ 5 } 5 } - \frac{ { \left( \frac{ 1 }{ 2 } \right) }^{ 4 } { \left( \frac{ 1 }{ 2 } \right) }^{ 3 } { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } }{ { \left( \frac{ 1 }{ 2 } \right) }^{ 5 } { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } }$$

Evaluate

$$24$$

Solution Steps

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

$$\frac{5^{5}\times 5^{7}}{5^{4}\times 5^{5}\times 5}-\frac{\left(\frac{1}{2}\right)^{4}\times \left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{2}\right)^{2}}{\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$\frac{5^{12}}{5^{4}\times 5^{5}\times 5}-\frac{\left(\frac{1}{2}\right)^{4}\times \left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{2}\right)^{2}}{\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{5^{12}}{5^{9}\times 5}-\frac{\left(\frac{1}{2}\right)^{4}\times \left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{2}\right)^{2}}{\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{5^{12}}{5^{10}}-\frac{\left(\frac{1}{2}\right)^{4}\times \left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{2}\right)^{2}}{\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 12 to get 2.

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$5^{2}-\frac{\left(\frac{1}{2}\right)^{7}\times \left(\frac{1}{2}\right)^{2}}{\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$5^{2}-\frac{\left(\frac{1}{2}\right)^{9}}{\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$5^{2}-\frac{\left(\frac{1}{2}\right)^{9}}{\left(\frac{1}{2}\right)^{7}\times \left(\frac{1}{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$5^{2}-\frac{\left(\frac{1}{2}\right)^{9}}{\left(\frac{1}{2}\right)^{9}}$$

Divide \left(\frac{1}{2}\right)^{9} by \left(\frac{1}{2}\right)^{9} to get 1.

$$5^{2}-1$$

Calculate 5 to the power of 2 and get 25.

$$25-1$$

Subtract 1 from 25 to get 24.

$$24$$

Factor

$$2^{3}\times 3$$