Solve (2a^2b^2)^2divab^3*3a

$$( 2 a ^ { 2 } b ^ { 2 } ) ^ { 2 } \div a b ^ { 3 } \times 3 a$$

Evaluate

$$12a^{4}b^{7}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{2}a^{4}b^{4}}{a}b^{3}\times 3a$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{4}}{a}b^{3}\times 3a$$

Cancel out a in both numerator and denominator.

$$4a^{3}b^{4}b^{3}\times 3a$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$4a^{3}b^{7}\times 3a$$

Multiply 4 and 3 to get 12.

$$12a^{3}b^{7}a$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$12a^{4}b^{7}$$

Expand

$$12a^{4}b^{7}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{2}a^{4}b^{4}}{a}b^{3}\times 3a$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{4}}{a}b^{3}\times 3a$$

Cancel out a in both numerator and denominator.

$$4a^{3}b^{4}b^{3}\times 3a$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$4a^{3}b^{7}\times 3a$$

Multiply 4 and 3 to get 12.

$$12a^{3}b^{7}a$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$12a^{4}b^{7}$$