Evaluate (45(4)^(3/2))/2-(21(4)^(1/2))/2

$\frac{45 {(4)}^{\frac{3}{2}}}{2} - \frac{21 {(4)}^{\frac{1}{2}}}{2}$

Step 1

Combine the numerators over the common denominator.

$\frac{45 {(4)}^{\frac{3}{2}} - 21 {(4)}^{\frac{1}{2}}}{2}$

Step 2

Simplify each term.

Rewrite $4$ as $2^{2}$ .

$\frac{45 {(2^{2})}^{\frac{3}{2}} - 21 {(4)}^{\frac{1}{2}}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{45 \cdot 2^{2 (\frac{3}{2})} - 21 {(4)}^{\frac{1}{2}}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{45 \cdot 2^{2 (\frac{3}{2})} - 21 {(4)}^{\frac{1}{2}}}{2}$

Rewrite the expression.

$\frac{45 \cdot 2^{3} - 21 {(4)}^{\frac{1}{2}}}{2}$

Raise $2$ to the power of $3$ .

$\frac{45 \cdot 8 - 21 {(4)}^{\frac{1}{2}}}{2}$

Multiply $45$ by $8$ .

$\frac{360 - 21 {(4)}^{\frac{1}{2}}}{2}$

Rewrite $4$ as $2^{2}$ .

$\frac{360 - 21 {(2^{2})}^{\frac{1}{2}}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{360 - 21 \cdot 2^{2 (\frac{1}{2})}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{360 - 21 \cdot 2^{2 (\frac{1}{2})}}{2}$

Rewrite the expression.

$\frac{360 - 21 \cdot 2^{1}}{2}$

Evaluate the exponent.

$\frac{360 - 21 \cdot 2}{2}$

Multiply $- 21$ by $2$ .

$\frac{360 - 42}{2}$

Step 3

Simplify the expression.

Subtract $42$ from $360$ .

$\frac{318}{2}$

Divide $318$ by $2$ .

$159$