Calculate: 24^2\div2^5+10^3\div40+2^2 \times 3^3 \times 5^2\div30^2

Expression: ${24}^{2}\div{2}^{5}+{10}^{3}\div40+{2}^{2} \times {3}^{3} \times {5}^{2}\div{30}^{2}$

Write the division as a fraction

$\frac{ {24}^{2} }{ {2}^{5} }+{10}^{3}\div40+{2}^{2} \times {3}^{3} \times {5}^{2}\div{30}^{2}$

Write the division as a fraction

$\frac{ {24}^{2} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+{2}^{2} \times {3}^{3} \times {5}^{2}\div{30}^{2}$

Write the division as a fraction

$\frac{ {24}^{2} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+\frac{ {2}^{2} \times {3}^{3} \times {5}^{2} }{ {30}^{2} }$

Factor the expression

$\frac{ {6}^{2} \times {4}^{2} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+\frac{ {2}^{2} \times {3}^{3} \times {5}^{2} }{ {30}^{2} }$

Factor the expression

$\frac{ {6}^{2} \times {4}^{2} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+\frac{ {2}^{2} \times {3}^{3} \times {5}^{2} }{ {15}^{2} \times {2}^{2} }$

Write the expression in exponential form with the base of $2$

$\frac{ {6}^{2} \times {2}^{4} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+\frac{ {2}^{2} \times {3}^{3} \times {5}^{2} }{ {15}^{2} \times {2}^{2} }$

Factor the expression

$\frac{ {6}^{2} \times {2}^{4} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+\frac{ {2}^{2} \times {3}^{3} \times {5}^{2} }{ {5}^{2} \times {3}^{2} \times {2}^{2} }$

Cancel out the common factor ${2}^{2}$

$\frac{ {6}^{2} \times {2}^{4} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+\frac{ {3}^{3} \times {5}^{2} }{ {5}^{2} \times {3}^{2} }$

Evaluate the power

$\frac{ 36 \times {2}^{4} }{ {2}^{5} }+\frac{ {10}^{3} }{ 40 }+\frac{ {3}^{3} \times {5}^{2} }{ {5}^{2} \times {3}^{2} }$

Simplify the expression

$\frac{ 36 }{ 2 }+\frac{ {10}^{3} }{ 40 }+\frac{ {3}^{3} \times {5}^{2} }{ {5}^{2} \times {3}^{2} }$

Cancel out the common factor ${5}^{2}$

$\frac{ 36 }{ 2 }+\frac{ {10}^{3} }{ 40 }+\frac{ {3}^{3} }{ {3}^{2} }$

Simplify the expression

$\frac{ 36 }{ 2 }+\frac{ {10}^{3} }{ 40 }+3$

Cancel out the common factor $2$

$18+\frac{ {10}^{3} }{ 40 }+3$

Add the numbers

$21+\frac{ {10}^{3} }{ 40 }$

Evaluate the power

$21+\frac{ 1000 }{ 40 }$

Cancel out the common factor $40$

$21+25$

Add the numbers

$46$