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

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

Evaluate

$$a^{26}b^{30}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\left(\left(-a^{4}\right)b^{3}\right)^{3}\left(\left(-a^{2}\right)b^{3}\right)^{7}$$

Expand \left(\left(-a^{4}\right)b^{3}\right)^{3}.

$$\left(-a^{4}\right)^{3}\left(b^{3}\right)^{3}\left(\left(-a^{2}\right)b^{3}\right)^{7}$$

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

$$\left(-a^{4}\right)^{3}b^{9}\left(\left(-a^{2}\right)b^{3}\right)^{7}$$

Expand \left(\left(-a^{2}\right)b^{3}\right)^{7}.

$$\left(-a^{4}\right)^{3}b^{9}\left(-a^{2}\right)^{7}\left(b^{3}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.

$$\left(-a^{4}\right)^{3}b^{9}\left(-a^{2}\right)^{7}b^{21}$$

To multiply powers of the same base, add their exponents. Add 9 and 21 to get 30.

$$\left(-a^{4}\right)^{3}b^{30}\left(-a^{2}\right)^{7}$$

Expand \left(-a^{4}\right)^{3}.

$$\left(-1\right)^{3}\left(a^{4}\right)^{3}b^{30}\left(-a^{2}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-1\right)^{3}a^{12}b^{30}\left(-a^{2}\right)^{7}$$

Calculate -1 to the power of 3 and get -1.

$$-a^{12}b^{30}\left(-a^{2}\right)^{7}$$

Expand \left(-a^{2}\right)^{7}.

$$-a^{12}b^{30}\left(-1\right)^{7}\left(a^{2}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 7 to get 14.

$$-a^{12}b^{30}\left(-1\right)^{7}a^{14}$$

Calculate -1 to the power of 7 and get -1.

$$-a^{12}b^{30}\left(-1\right)a^{14}$$

Multiply -1 and -1 to get 1.

$$a^{12}b^{30}a^{14}$$

To multiply powers of the same base, add their exponents. Add 12 and 14 to get 26.

$$a^{26}b^{30}$$

Expand

$$a^{26}b^{30}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\left(\left(-a^{4}\right)b^{3}\right)^{3}\left(\left(-a^{2}\right)b^{3}\right)^{7}$$

Expand \left(\left(-a^{4}\right)b^{3}\right)^{3}.

$$\left(-a^{4}\right)^{3}\left(b^{3}\right)^{3}\left(\left(-a^{2}\right)b^{3}\right)^{7}$$

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

$$\left(-a^{4}\right)^{3}b^{9}\left(\left(-a^{2}\right)b^{3}\right)^{7}$$

Expand \left(\left(-a^{2}\right)b^{3}\right)^{7}.

$$\left(-a^{4}\right)^{3}b^{9}\left(-a^{2}\right)^{7}\left(b^{3}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.

$$\left(-a^{4}\right)^{3}b^{9}\left(-a^{2}\right)^{7}b^{21}$$

To multiply powers of the same base, add their exponents. Add 9 and 21 to get 30.

$$\left(-a^{4}\right)^{3}b^{30}\left(-a^{2}\right)^{7}$$

Expand \left(-a^{4}\right)^{3}.

$$\left(-1\right)^{3}\left(a^{4}\right)^{3}b^{30}\left(-a^{2}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-1\right)^{3}a^{12}b^{30}\left(-a^{2}\right)^{7}$$

Calculate -1 to the power of 3 and get -1.

$$-a^{12}b^{30}\left(-a^{2}\right)^{7}$$

Expand \left(-a^{2}\right)^{7}.

$$-a^{12}b^{30}\left(-1\right)^{7}\left(a^{2}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 7 to get 14.

$$-a^{12}b^{30}\left(-1\right)^{7}a^{14}$$

Calculate -1 to the power of 7 and get -1.

$$-a^{12}b^{30}\left(-1\right)a^{14}$$

Multiply -1 and -1 to get 1.

$$a^{12}b^{30}a^{14}$$

To multiply powers of the same base, add their exponents. Add 12 and 14 to get 26.

$$a^{26}b^{30}$$