Algebra Examples

$\frac{5}{8} + \frac{1}{2} {(\frac{3}{4})}^{2}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{3}{4}$ .

$\frac{5}{8} + \frac{1}{2} \cdot \frac{3^{2}}{4^{2}}$

Step 1.2

Combine.

$\frac{5}{8} + \frac{1 \cdot 3^{2}}{2 \cdot 4^{2}}$

Step 1.3

Multiply $3^{2}$ by $1$ .

$\frac{5}{8} + \frac{3^{2}}{2 \cdot 4^{2}}$

Step 1.4

Simplify the denominator.

Tap for more steps...

Step 1.4.1

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

$\frac{5}{8} + \frac{3^{2}}{2 \cdot {(2^{2})}^{2}}$

Step 1.4.2

Multiply the exponents in ${(2^{2})}^{2}$ .

Tap for more steps...

Step 1.4.2.1

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

$\frac{5}{8} + \frac{3^{2}}{2 \cdot 2^{2 \cdot 2}}$

Step 1.4.2.2

Multiply $2$ by $2$ .

$\frac{5}{8} + \frac{3^{2}}{2 \cdot 2^{4}}$

Step 1.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5}{8} + \frac{3^{2}}{2^{1 + 4}}$

Step 1.4.4

Add $1$ and $4$ .

$\frac{5}{8} + \frac{3^{2}}{2^{5}}$

Step 1.5

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

$\frac{5}{8} + \frac{9}{2^{5}}$

Step 1.6

Raise $2$ to the power of $5$ .

$\frac{5}{8} + \frac{9}{32}$

Step 2

To write $\frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{8} \cdot \frac{4}{4} + \frac{9}{32}$

Step 3

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{5}{8}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 4}{8 \cdot 4} + \frac{9}{32}$

Step 3.2

Multiply $8$ by $4$ .

$\frac{5 \cdot 4}{32} + \frac{9}{32}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + 9}{32}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $5$ by $4$ .

$\frac{20 + 9}{32}$

Step 5.2

Add $20$ and $9$ .

$\frac{29}{32}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{32}$

Decimal Form:

$0.90625$