What is (((-2x)^2)/(3xy^2))^3 ?

The solution to (((-2x)^2)/(3xy^2))^3 is (64x^3)/(27y^6)

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simplify (((-2x)^2)/(3xy^2))^3

simplify

(\frac{( - 2 x ) ^{2}}{3 x y ^{2}})^{3}

\frac{64 x ^{3}}{27 y ^{6}}

Solution steps

(\frac{( - 2 x ) ^{2}}{3 x y ^{2}})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( ( - 2 x ) ^{2} ) ^{3}}{( 3 x y ^{2} ) ^{3}}

Simplify

((- 2 x)^{2})^{3} : 64 x^{6}

= \frac{64 x ^{6}}{( 3 x y ^{2} ) ^{3}}

Simplify

(3 x y^{2})^{3} : 27 x^{3} y^{6}

= \frac{64 x ^{6}}{27 x ^{3} y ^{6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{x ^{6}}{x ^{3}} = x^{6 - 3}

= \frac{64 x ^{6 - 3}}{27 y ^{6}}

Subtract the numbers:

6 - 3 = 3

= \frac{64 x ^{3}}{27 y ^{6}}

x^{3} - 2 x^{2} + 1

- 3 (x - 1) + 8 (x - 3) = 6 x + 7 - 5 x

6 \leq x \leq 7

- 4 > 4

1 - x^{2} > x - 1

What is (((-2x)^2)/(3xy^2))^3 ?
The solution to (((-2x)^2)/(3xy^2))^3 is (64x^3)/(27y^6)