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

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

Evaluate

$$\frac{1}{b^{6}a^{9}}$$

Solution Steps

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

$$\left(a^{5}b^{2}\right)^{-3}a^{6}$$

Expand \left(a^{5}b^{2}\right)^{-3}.

$$\left(a^{5}\right)^{-3}\left(b^{2}\right)^{-3}a^{6}$$

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

$$a^{-15}\left(b^{2}\right)^{-3}a^{6}$$

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

$$a^{-15}b^{-6}a^{6}$$

To multiply powers of the same base, add their exponents. Add -15 and 6 to get -9.

$$a^{-9}b^{-6}$$

Expand

$$\frac{1}{b^{6}a^{9}}$$

Solution Steps

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

$$\left(a^{5}b^{2}\right)^{-3}a^{6}$$

Expand \left(a^{5}b^{2}\right)^{-3}.

$$\left(a^{5}\right)^{-3}\left(b^{2}\right)^{-3}a^{6}$$

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

$$a^{-15}\left(b^{2}\right)^{-3}a^{6}$$

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

$$a^{-15}b^{-6}a^{6}$$

To multiply powers of the same base, add their exponents. Add -15 and 6 to get -9.

$$a^{-9}b^{-6}$$