Solve frac{a^{-6}(-a)^4(-a)^5}{(-a)^-3(-a)^-2}

$$\frac { a ^ { - 6 } ( - a ) ^ { 4 } ( - a ) ^ { 5 } } { ( - a ) ^ { - 3 } ( - a ) ^ { - 2 } }$$

Evaluate

$$a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{a^{-6}\left(-a\right)^{9}}{\left(-a\right)^{-3}\left(-a\right)^{-2}}$$

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$\frac{a^{-6}\left(-a\right)^{9}}{\left(-a\right)^{-5}}$$

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

$$a^{-6}\left(-a\right)^{14}$$

Expand \left(-a\right)^{14}.

$$a^{-6}\left(-1\right)^{14}a^{14}$$

Calculate -1 to the power of 14 and get 1.

$$a^{-6}\times 1a^{14}$$

To multiply powers of the same base, add their exponents. Add -6 and 14 to get 8.

$$a^{8}\times 1$$

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

$$a^{8}$$

Expand

$$a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{a^{-6}\left(-a\right)^{9}}{\left(-a\right)^{-3}\left(-a\right)^{-2}}$$

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$\frac{a^{-6}\left(-a\right)^{9}}{\left(-a\right)^{-5}}$$

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

$$a^{-6}\left(-a\right)^{14}$$

Expand \left(-a\right)^{14}.

$$a^{-6}\left(-1\right)^{14}a^{14}$$

Calculate -1 to the power of 14 and get 1.

$$a^{-6}\times 1a^{14}$$

To multiply powers of the same base, add their exponents. Add -6 and 14 to get 8.

$$a^{8}\times 1$$

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

$$a^{8}$$