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

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

Step 1

Simplify each term.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{2}{3} \cdot 8 - 4 {(4)}^{\frac{1}{2}}$

Multiply $\frac{2}{3} \cdot 8$ .

Combine $\frac{2}{3}$ and $8$ .

$\frac{2 \cdot 8}{3} - 4 {(4)}^{\frac{1}{2}}$

Multiply $2$ by $8$ .

$\frac{16}{3} - 4 {(4)}^{\frac{1}{2}}$

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

$\frac{16}{3} - 4 {(2^{2})}^{\frac{1}{2}}$

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

$\frac{16}{3} - 4 \cdot 2^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{16}{3} - 4 \cdot 2^{2 (\frac{1}{2})}$

Rewrite the expression.

$\frac{16}{3} - 4 \cdot 2^{1}$

Evaluate the exponent.

$\frac{16}{3} - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$\frac{16}{3} - 8$

Step 2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{16}{3} - 8 \cdot \frac{3}{3}$

Step 3

Combine $- 8$ and $\frac{3}{3}$ .

$\frac{16}{3} + \frac{- 8 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{16 - 8 \cdot 3}{3}$

Step 5

Simplify the numerator.

Multiply $- 8$ by $3$ .

$\frac{16 - 24}{3}$

Subtract $24$ from $16$ .

$\frac{- 8}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{8}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{3}$

Decimal Form:

$- 2.\overline{6}$

Mixed Number Form:

$- 2 \frac{2}{3}$

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

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