Solve (49a^4*b^12)^frac{1{2}}=

$$( 49 a ^ { 4 } \cdot b ^ { 12 } ) ^ { \frac { 1 } { 2 } } =$$

Evaluate

$$7a^{2}b^{6}$$

Solution Steps

Expand \left(49a^{4}b^{12}\right)^{\frac{1}{2}}.

$$49^{\frac{1}{2}}\left(a^{4}\right)^{\frac{1}{2}}\left(b^{12}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{1}{2} to get 2.

$$49^{\frac{1}{2}}a^{2}\left(b^{12}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 12 and \frac{1}{2} to get 6.

$$49^{\frac{1}{2}}a^{2}b^{6}$$

Calculate 49 to the power of \frac{1}{2} and get 7.

$$7a^{2}b^{6}$$

Differentiate w.r.t. b

$$42a^{2}b^{5}$$