Solve frac{(5^{-1}ab)^-1}{(10a^-2b^3)^-2}

$$\frac { ( 5 ^ { - 1 } a b ) ^ { - 1 } } { ( 10 a ^ { - 2 } b ^ { 3 } ) ^ { - 2 } }$$

Evaluate

$$500\times \left(\frac{b}{a}\right)^{5}$$

Solution Steps

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{\left(\frac{1}{5}ab\right)^{-1}}{\left(10a^{-2}b^{3}\right)^{-2}}$$

Expand \left(\frac{1}{5}ab\right)^{-1}.

$$\frac{\left(\frac{1}{5}\right)^{-1}a^{-1}b^{-1}}{\left(10a^{-2}b^{3}\right)^{-2}}$$

Calculate \frac{1}{5} to the power of -1 and get 5.

$$\frac{5a^{-1}b^{-1}}{\left(10a^{-2}b^{3}\right)^{-2}}$$

Expand \left(10a^{-2}b^{3}\right)^{-2}.

$$\frac{5a^{-1}b^{-1}}{10^{-2}\left(a^{-2}\right)^{-2}\left(b^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{5a^{-1}b^{-1}}{10^{-2}a^{4}b^{-6}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{5a^{-1}b^{-1}}{\frac{1}{100}a^{4}b^{-6}}$$

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

$$\frac{5\times \frac{1}{a}b^{5}}{\frac{1}{100}a^{4}}$$

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

$$\frac{5b^{5}}{\frac{1}{100}a^{5}}$$

Expand

$$500\times \left(\frac{b}{a}\right)^{5}$$

Solution Steps

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{\left(\frac{1}{5}ab\right)^{-1}}{\left(10a^{-2}b^{3}\right)^{-2}}$$

Expand \left(\frac{1}{5}ab\right)^{-1}.

$$\frac{\left(\frac{1}{5}\right)^{-1}a^{-1}b^{-1}}{\left(10a^{-2}b^{3}\right)^{-2}}$$

Calculate \frac{1}{5} to the power of -1 and get 5.

$$\frac{5a^{-1}b^{-1}}{\left(10a^{-2}b^{3}\right)^{-2}}$$

Expand \left(10a^{-2}b^{3}\right)^{-2}.

$$\frac{5a^{-1}b^{-1}}{10^{-2}\left(a^{-2}\right)^{-2}\left(b^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{5a^{-1}b^{-1}}{10^{-2}a^{4}b^{-6}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{5a^{-1}b^{-1}}{\frac{1}{100}a^{4}b^{-6}}$$

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

$$\frac{5\times \frac{1}{a}b^{5}}{\frac{1}{100}a^{4}}$$

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

$$\frac{5b^{5}}{\frac{1}{100}a^{5}}$$