Solve 8^-1a^2b^-2/{left(2ab^-1right)^-3}

$$\frac{ { 8 }^{ -1 } { a }^{ 2 } { b }^{ -2 } }{ { \left(2a { b }^{ -1 } \right) }^{ -3 } }$$

Evaluate

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

Short Solution Steps

Calculate 8 to the power of -1 and get \frac{1}{8}.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{\left(2ab^{-1}\right)^{-3}}$$

Expand \left(2ab^{-1}\right)^{-3}.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{2^{-3}a^{-3}\left(b^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{2^{-3}a^{-3}b^{3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{\frac{1}{8}a^{-3}b^{3}}$$

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

$$\frac{\frac{1}{8}b^{-2}a^{5}}{\frac{1}{8}b^{3}}$$

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

$$\frac{a^{5}}{\left(\frac{1}{8}\right)^{0}b^{5}}$$

Calculate \frac{1}{8} to the power of 0 and get 1.

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

For any term t, t\times 1=t and 1t=t.

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

Expand

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

Short Solution Steps

Calculate 8 to the power of -1 and get \frac{1}{8}.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{\left(2ab^{-1}\right)^{-3}}$$

Expand \left(2ab^{-1}\right)^{-3}.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{2^{-3}a^{-3}\left(b^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{2^{-3}a^{-3}b^{3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}a^{2}b^{-2}}{\frac{1}{8}a^{-3}b^{3}}$$

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

$$\frac{\frac{1}{8}b^{-2}a^{5}}{\frac{1}{8}b^{3}}$$

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

$$\frac{a^{5}}{\left(\frac{1}{8}\right)^{0}b^{5}}$$

Calculate \frac{1}{8} to the power of 0 and get 1.

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

For any term t, t\times 1=t and 1t=t.

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