simplify (27x^6)^{2/3} — step-by-step solution

⚠ (27x^6)^{2/3} is read as (27x^6)^(2/3): use ^(...) to group an exponent, use * to multiply

Let's reduce:

{(27 x^{6})}^{\frac{2}{3}}

ⓘ The power of a product is the product of the powers:

{(27 x^{6})}^{\frac{2}{3}}

27^{\frac{2}{3}} \cdot {(x^{6})}^{\frac{2}{3}}

27^{\frac{2}{3}} \cdot {(x^{6})}^{\frac{2}{3}}

ⓘ An exponent m/n means taking the nth root and then the mth power; here, the root of order

3

27

3

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

3^{2}

■A power of a power multiplies the exponents, (a^n)^m = a^(n*m):

{(x^{6})}^{\frac{2}{3}}

x^{6 \cdot \frac{2}{3}}

3^{2} \cdot x^{6 \cdot \frac{2}{3}}

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

3^{2}

3 \cdot 3

9

■Multiplying a fraction by a number multiplies its numerator:

6 \cdot \frac{2}{3}

\frac{6 \cdot 2}{3}

\frac{12}{3}

9 x^{\frac{12}{3}}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{12}{3}

4

▶Simplified form:

9 x^{4}