Solve frac{a^{4}*b^-2}{(a^-3b^5)^3}

$$\frac { a ^ { 4 } \cdot b ^ { - 2 } } { ( a ^ { - 3 } b ^ { 5 } ) ^ { 3 } }$$

Evaluate

$$\frac{a^{13}}{b^{17}}$$

Solution Steps

Expand \left(a^{-3}b^{5}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{a^{4}b^{-2}}{a^{-9}\left(b^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{a^{4}b^{-2}}{a^{-9}b^{15}}$$

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

$$\frac{b^{-2}a^{13}}{b^{15}}$$

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

$$\frac{a^{13}}{b^{17}}$$

Expand

$$\frac{a^{13}}{b^{17}}$$

Solution Steps

Expand \left(a^{-3}b^{5}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{a^{4}b^{-2}}{a^{-9}\left(b^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{a^{4}b^{-2}}{a^{-9}b^{15}}$$

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

$$\frac{b^{-2}a^{13}}{b^{15}}$$

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

$$\frac{a^{13}}{b^{17}}$$