simplify (1/2)^3+(2/3)^2 — step-by-step solution

Let's reduce:

{(\frac{1}{2})}^{3} + {(\frac{2}{3})}^{2}

ⓘ The power of a quotient is the quotient of the powers, (a/b)^n = a^n/b^n:

{(\frac{1}{2})}^{3}

\frac{1}{2^{3}}

{(\frac{2}{3})}^{2}

\frac{2^{2}}{3^{2}}

\frac{1}{2^{3}} + \frac{2^{2}}{3^{2}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

2^{3}

2 \times 2 \times 2

8

2^{2}

2 \times 2

4

3^{2}

3 \times 3

9

\frac{1}{8} + \frac{4}{9}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

72

, the least common multiple of

8

and

9

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{1}{8} + \frac{4}{9}

\frac{1 \times 9}{8 \times 9} + \frac{4 \times 8}{9 \times 8}

\frac{1 \times 9 + 4 \times 8}{8 \times 9}

\frac{9 + 4 \times 8}{8 \times 9}

\frac{9 + 4 \times 8}{8 \times 9}

ⓘ Multiplications are done before additions and subtractions:

4 \times 8

32

ⅰ

8 \times 9

72

\frac{9 + 32}{72}

ⓘ The numerator and the denominator are computed before the division:

9 + 32

41

▶Simplified form:

\frac{41}{72}

The numeric value of:

\frac{41}{72}

is:

▷

\approx 0.5694