Solve (-a)^{2}*(a^2)^-5*((-a)^-1)^-2

$$( - a ) ^ { 2 } \cdot ( a ^ { 2 } ) ^ { - 5 } \cdot ( ( - a ) ^ { - 1 } ) ^ { - 2 }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.

$$\left(-a\right)^{2}a^{-10}\left(\left(-a\right)^{-1}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\left(-a\right)^{2}a^{-10}\left(-a\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\left(-a\right)^{4}a^{-10}$$

Expand \left(-a\right)^{4}.

$$\left(-1\right)^{4}a^{4}a^{-10}$$

Calculate -1 to the power of 4 and get 1.

$$1a^{4}a^{-10}$$

To multiply powers of the same base, add their exponents. Add 4 and -10 to get -6.

$$1a^{-6}$$

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

$$a^{-6}$$

Expand

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.

$$\left(-a\right)^{2}a^{-10}\left(\left(-a\right)^{-1}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\left(-a\right)^{2}a^{-10}\left(-a\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\left(-a\right)^{4}a^{-10}$$

Expand \left(-a\right)^{4}.

$$\left(-1\right)^{4}a^{4}a^{-10}$$

Calculate -1 to the power of 4 and get 1.

$$1a^{4}a^{-10}$$

To multiply powers of the same base, add their exponents. Add 4 and -10 to get -6.

$$1a^{-6}$$

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

$$a^{-6}$$