simplify (16/3)^3-8(16/3)^2 — step-by-step solution

Let's reduce:

{(\frac{16}{3})}^{3} - 8 \times {(\frac{16}{3})}^{2}

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

{(\frac{16}{3})}^{3}

\frac{16^{3}}{3^{3}}

{(\frac{16}{3})}^{2}

\frac{16^{2}}{3^{2}}

\frac{16^{3}}{3^{3}} - 8 \times \frac{16^{2}}{3^{2}}

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

16^{3}

16 \times 16 \times 16

4096

3^{3}

3 \times 3 \times 3

27

16^{2}

16 \times 16

256

3^{2}

3 \times 3

9

\frac{4096}{27} - 8 \times \frac{256}{9}

ⓘ Multiplying a fraction by a number multiplies its numerator:

8 \times \frac{256}{9}

\frac{8 \times 256}{9}

\frac{2048}{9}

\frac{4096}{27} - \frac{2048}{9}

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

27

, the least common multiple of

27

and

9

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

\frac{4096}{27} - \frac{2048}{9}

\frac{4096}{27} + \frac{-2048 \times 3}{9 \times 3}

\frac{4096 - 2048 \times 3}{27}

\frac{4096 - 2048 \times 3}{27}

ⓘ Multiplications are done before additions and subtractions:

2048 \times 3

(2000 + 40 + 8) \times 3

2000 \times 3 + 40 \times 3 + 8 \times 3

6000 + 120 + 24

6144

\frac{4096 - 6144}{27}

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

4096 - 6144

-2048

▶Simplified form:

- \frac{2048}{27}

The numeric value of:

- \frac{2048}{27}

is:

▷

\approx -75.8519