Evaluate (1/4)^3+(1/3)^3-(7/12)^3

${(\frac{1}{4})}^{3} + {(\frac{1}{3})}^{3} - {(\frac{7}{12})}^{3}$

Step 1

Simplify each term.

Apply the product rule to $\frac{1}{4}$ .

$\frac{1^{3}}{4^{3}} + {(\frac{1}{3})}^{3} - {(\frac{7}{12})}^{3}$

One to any power is one.

$\frac{1}{4^{3}} + {(\frac{1}{3})}^{3} - {(\frac{7}{12})}^{3}$

Raise $4$ to the power of $3$ .

$\frac{1}{64} + {(\frac{1}{3})}^{3} - {(\frac{7}{12})}^{3}$

Apply the product rule to $\frac{1}{3}$ .

$\frac{1}{64} + \frac{1^{3}}{3^{3}} - {(\frac{7}{12})}^{3}$

One to any power is one.

$\frac{1}{64} + \frac{1}{3^{3}} - {(\frac{7}{12})}^{3}$

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

$\frac{1}{64} + \frac{1}{27} - {(\frac{7}{12})}^{3}$

Apply the product rule to $\frac{7}{12}$ .

$\frac{1}{64} + \frac{1}{27} - \frac{7^{3}}{12^{3}}$

Raise $7$ to the power of $3$ .

$\frac{1}{64} + \frac{1}{27} - \frac{343}{12^{3}}$

Raise $12$ to the power of $3$ .

$\frac{1}{64} + \frac{1}{27} - \frac{343}{1728}$

Step 2

Find the common denominator.

Multiply $\frac{1}{64}$ by $\frac{27}{27}$ .

$\frac{1}{64} \cdot \frac{27}{27} + \frac{1}{27} - \frac{343}{1728}$

Multiply $\frac{1}{64}$ by $\frac{27}{27}$ .

$\frac{27}{64 \cdot 27} + \frac{1}{27} - \frac{343}{1728}$

Multiply $\frac{1}{27}$ by $\frac{64}{64}$ .

$\frac{27}{64 \cdot 27} + \frac{1}{27} \cdot \frac{64}{64} - \frac{343}{1728}$

Multiply $\frac{1}{27}$ by $\frac{64}{64}$ .

$\frac{27}{64 \cdot 27} + \frac{64}{27 \cdot 64} - \frac{343}{1728}$

Reorder the factors of $64 \cdot 27$ .

$\frac{27}{27 \cdot 64} + \frac{64}{27 \cdot 64} - \frac{343}{1728}$

Multiply $27$ by $64$ .

$\frac{27}{1728} + \frac{64}{27 \cdot 64} - \frac{343}{1728}$

Multiply $27$ by $64$ .

$\frac{27}{1728} + \frac{64}{1728} - \frac{343}{1728}$

Step 3

Combine the numerators over the common denominator.

$\frac{27 + 64 - 343}{1728}$

Step 4

Simplify by adding and subtracting.

Add $27$ and $64$ .

$\frac{91 - 343}{1728}$

Subtract $343$ from $91$ .

$\frac{- 252}{1728}$

Step 5

Cancel the common factor of $- 252$ and $1728$ .

Factor $36$ out of $- 252$ .

$\frac{36 (- 7)}{1728}$

Cancel the common factors.

Factor $36$ out of $1728$ .

$\frac{36 \cdot - 7}{36 \cdot 48}$

Cancel the common factor.

$\frac{36 \cdot - 7}{36 \cdot 48}$

Rewrite the expression.

$\frac{- 7}{48}$

Step 6

Move the negative in front of the fraction.

$- \frac{7}{48}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{48}$

Decimal Form:

$- 0.1458\overline{3}$

Evaluate (1/4)^3+(1/3)^3-(7/12)^3

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