Solve (7a^{2}b^3)^2/a^3b^5

$$( 7 a ^ { 2 } b ^ { 3 } ) ^ { 2 } / a ^ { 3 } b ^ { 5 }$$

Evaluate

$$49ab^{11}$$

Solution Steps

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

$$\frac{7^{2}\left(a^{2}\right)^{2}\left(b^{3}\right)^{2}}{a^{3}}b^{5}$$

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

$$\frac{7^{2}a^{4}\left(b^{3}\right)^{2}}{a^{3}}b^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{7^{2}a^{4}b^{6}}{a^{3}}b^{5}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49a^{4}b^{6}}{a^{3}}b^{5}$$

Cancel out a^{3} in both numerator and denominator.

$$49ab^{6}b^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$49ab^{11}$$

Expand

$$49ab^{11}$$

Solution Steps

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

$$\frac{7^{2}\left(a^{2}\right)^{2}\left(b^{3}\right)^{2}}{a^{3}}b^{5}$$

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

$$\frac{7^{2}a^{4}\left(b^{3}\right)^{2}}{a^{3}}b^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{7^{2}a^{4}b^{6}}{a^{3}}b^{5}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49a^{4}b^{6}}{a^{3}}b^{5}$$

Cancel out a^{3} in both numerator and denominator.

$$49ab^{6}b^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$49ab^{11}$$