Work out the value of \( \left(5 \times 10^{3}\right) \times\left(6 \times 10^{7}\right) \) Give your answer in standard form.

To find the value of \( \left(5 \times 10^{3}\right) \times\left(6 \times 10^{7}\right) \), we can separate the constants and the powers of ten. First, multiply the constants: \( 5 \times 6 = 30 \). Next, multiply the powers of ten: \( 10^{3} \times 10^{7} = 10^{(3+7)} = 10^{10} \). Now we can combine these results: \( 30 \times 10^{10} \). To express this in standard form, we convert \( 30 \) to \( 3.0 \times 10^{1} \): \[ 30 \times 10^{10} = (3.0 \times 10^{1}) \times 10^{10} = 3.0 \times 10^{(1+10)} = 3.0 \times 10^{11}. \] Thus, the final answer in standard form is: \[ \boxed{3.0 \times 10^{11}}. \]