Solve [(-a^{3}b^{3})^3]^3*(-ab^2)^2

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

Evaluate

$$-a^{29}b^{31}$$

Solution Steps

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

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

Expand \left(\left(-a^{3}\right)b^{3}\right)^{9}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 9 to get 27.

$$\left(-a^{3}\right)^{9}b^{27}\left(\left(-a\right)b^{2}\right)^{2}$$

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

$$\left(-a^{3}\right)^{9}b^{27}\left(-a\right)^{2}\left(b^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-a^{3}\right)^{9}b^{27}\left(-a\right)^{2}b^{4}$$

Calculate -a to the power of 2 and get a^{2}.

$$\left(-a^{3}\right)^{9}b^{27}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 27 and 4 to get 31.

$$\left(-a^{3}\right)^{9}b^{31}a^{2}$$

Expand \left(-a^{3}\right)^{9}.

$$\left(-1\right)^{9}\left(a^{3}\right)^{9}b^{31}a^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 9 to get 27.

$$\left(-1\right)^{9}a^{27}b^{31}a^{2}$$

Calculate -1 to the power of 9 and get -1.

$$-a^{27}b^{31}a^{2}$$

To multiply powers of the same base, add their exponents. Add 27 and 2 to get 29.

$$-a^{29}b^{31}$$

Expand

$$-a^{29}b^{31}$$

Solution Steps

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

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

Expand \left(\left(-a^{3}\right)b^{3}\right)^{9}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 9 to get 27.

$$\left(-a^{3}\right)^{9}b^{27}\left(\left(-a\right)b^{2}\right)^{2}$$

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

$$\left(-a^{3}\right)^{9}b^{27}\left(-a\right)^{2}\left(b^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-a^{3}\right)^{9}b^{27}\left(-a\right)^{2}b^{4}$$

Calculate -a to the power of 2 and get a^{2}.

$$\left(-a^{3}\right)^{9}b^{27}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 27 and 4 to get 31.

$$\left(-a^{3}\right)^{9}b^{31}a^{2}$$

Expand \left(-a^{3}\right)^{9}.

$$\left(-1\right)^{9}\left(a^{3}\right)^{9}b^{31}a^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 9 to get 27.

$$\left(-1\right)^{9}a^{27}b^{31}a^{2}$$

Calculate -1 to the power of 9 and get -1.

$$-a^{27}b^{31}a^{2}$$

To multiply powers of the same base, add their exponents. Add 27 and 2 to get 29.

$$-a^{29}b^{31}$$