Solve (2a^8b^9*4ab^9)^3

$$( 2 a ^ { 8 } b ^ { 9 } \cdot 4 a b ^ { 9 } ) ^ { 3 }$$

Evaluate

$$512a^{27}b^{54}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

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

To multiply powers of the same base, add their exponents. Add 9 and 9 to get 18.

$$\left(2a^{9}b^{18}\times 4\right)^{3}$$

Multiply 2 and 4 to get 8.

$$\left(8a^{9}b^{18}\right)^{3}$$

Expand \left(8a^{9}b^{18}\right)^{3}.

$$8^{3}\left(a^{9}\right)^{3}\left(b^{18}\right)^{3}$$

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

$$8^{3}a^{27}\left(b^{18}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 18 and 3 to get 54.

$$8^{3}a^{27}b^{54}$$

Calculate 8 to the power of 3 and get 512.

$$512a^{27}b^{54}$$

Expand

$$512a^{27}b^{54}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

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

To multiply powers of the same base, add their exponents. Add 9 and 9 to get 18.

$$\left(2a^{9}b^{18}\times 4\right)^{3}$$

Multiply 2 and 4 to get 8.

$$\left(8a^{9}b^{18}\right)^{3}$$

Expand \left(8a^{9}b^{18}\right)^{3}.

$$8^{3}\left(a^{9}\right)^{3}\left(b^{18}\right)^{3}$$

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

$$8^{3}a^{27}\left(b^{18}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 18 and 3 to get 54.

$$8^{3}a^{27}b^{54}$$

Calculate 8 to the power of 3 and get 512.

$$512a^{27}b^{54}$$