Solve left(2^25^2right)^22^-2/{2^{3}{10}^2}=frac{{2}^2{5}^2}{{2}^3}

$$\frac{ { \left( { 2 }^{ 2 } { 5 }^{ 2 } \right) }^{ 2 } { 2 }^{ -2 } }{ { 2 }^{ 3 } { 10 }^{ 2 } } = \frac{ { 2 }^{ 2 } { 5 }^{ 2 } }{ { 2 }^{ 3 } }$$

Verify

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(4\times 25\right)^{2}}{2^{5}\times 10^{2}}=\frac{2^{2}\times 5^{2}}{2^{3}}$$

Multiply 4 and 25 to get 100.

$$\frac{100^{2}}{2^{5}\times 10^{2}}=\frac{2^{2}\times 5^{2}}{2^{3}}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{10000}{2^{5}\times 10^{2}}=\frac{2^{2}\times 5^{2}}{2^{3}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{10000}{32\times 10^{2}}=\frac{2^{2}\times 5^{2}}{2^{3}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{10000}{32\times 100}=\frac{2^{2}\times 5^{2}}{2^{3}}$$

Multiply 32 and 100 to get 3200.

$$\frac{10000}{3200}=\frac{2^{2}\times 5^{2}}{2^{3}}$$

Reduce the fraction \frac{10000}{3200} to lowest terms by extracting and canceling out 400.

$$\frac{25}{8}=\frac{2^{2}\times 5^{2}}{2^{3}}$$

Cancel out 2^{2} in both numerator and denominator.

$$\frac{25}{8}=\frac{5^{2}}{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25}{8}=\frac{25}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{25}{8} and \frac{25}{2} to fractions with denominator 8.

$$\frac{25}{8}=\frac{100}{8}$$

Compare \frac{25}{8} and \frac{100}{8}.

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