Solve B(frac{5^{3}*5^-2}{5^-1*5^4})^-2

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

Evaluate

$$625B$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add -1 and 4 to get 3.

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

Rewrite 5^{3} as 5^{1}\times 5^{2}. Cancel out 5^{1} in both numerator and denominator.

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

Calculate 5 to the power of 2 and get 25.

$$B\times \left(\frac{1}{25}\right)^{-2}$$

Calculate \frac{1}{25} to the power of -2 and get 625.

$$B\times 625$$

Expand

$$625B$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add -1 and 4 to get 3.

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

Rewrite 5^{3} as 5^{1}\times 5^{2}. Cancel out 5^{1} in both numerator and denominator.

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

Calculate 5 to the power of 2 and get 25.

$$B\times \left(\frac{1}{25}\right)^{-2}$$

Calculate \frac{1}{25} to the power of -2 and get 625.

$$B\times 625$$