What is simplify-6(2/3 p^8)^3 ?

The solution to simplify-6(2/3 p^8)^3 is -(16p^{24})/9

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simplify-6(2/3 p^8)^3

simplify

- 6 (\frac{2}{3} p^{8})^{3}

- \frac{16 p ^{24}}{9}

Solution steps

- 6 (\frac{2}{3} p^{8})^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(\frac{2}{3} p^{8})^{3} = (\frac{2}{3})^{3} (p^{8})^{3}

= - 6 (\frac{2}{3})^{3} (p^{8})^{3}

(\frac{2}{3})^{3} = \frac{8}{27}

= - 6 \cdot \frac{8}{27} (p^{8})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(p^{8})^{3} = p^{8 \cdot 3}

= - 6 \cdot \frac{8}{27} p^{8 \cdot 3}

Multiply the numbers:

8 \cdot 3 = 24

= - 6 \cdot \frac{8}{27} p^{24}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - 6 \cdot \frac{8 p ^{24}}{27}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{6 \cdot 8 p ^{24}}{27}

Cancel

- \frac{6 \cdot 8 p ^{24}}{27} : - \frac{2 \cdot 8 p ^{24}}{9}

= - \frac{2 \cdot 8 p ^{24}}{9}

Multiply the numbers:

2 \cdot 8 = 16

= - \frac{16 p ^{24}}{9}

16 + \frac{1}{9}

5 \times (- 10)

5 \times (- 25)

18 \times 6

18 \times 8

What is simplify-6(2/3 p^8)^3 ?
The solution to simplify-6(2/3 p^8)^3 is -(16p^{24})/9