What is ((5x^6y^2)/(10x^4y))^2 ?

The solution to ((5x^6y^2)/(10x^4y))^2 is (x^4y^2)/4

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simplify ((5x^6y^2)/(10x^4y))^2

simplify

(\frac{5 x ^{6} y ^{2}}{10 x ^{4} y})^{2}

\frac{x ^{4} y ^{2}}{4}

Solution steps

(\frac{5 x ^{6} y ^{2}}{10 x ^{4} y})^{2}

Apply exponent rule:

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

= \frac{( 5 x ^{6} y ^{2} ) ^{2}}{( 10 x ^{4} y ) ^{2}}

Simplify

(5 x^{6} y^{2})^{2} : 25 x^{12} y^{4}

= \frac{25 x ^{12} y ^{4}}{( 10 x ^{4} y ) ^{2}}

Simplify

(10 x^{4} y)^{2} : 100 x^{8} y^{2}

= \frac{25 x ^{12} y ^{4}}{100 x ^{8} y ^{2}}

Cancel the common factor:

25

= \frac{x ^{12} y ^{4}}{4 x ^{8} y ^{2}}

Apply exponent rule:

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

\frac{x ^{12}}{x ^{8}} = x^{12 - 8}

= \frac{y ^{4} x ^{12 - 8}}{4 y ^{2}}

Subtract the numbers:

12 - 8 = 4

= \frac{x ^{4} y ^{4}}{4 y ^{2}}

Apply exponent rule:

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

\frac{y ^{4}}{y ^{2}} = y^{4 - 2}

= \frac{x ^{4} y ^{4 - 2}}{4}

Subtract the numbers:

4 - 2 = 2

= \frac{x ^{4} y ^{2}}{4}

x^{2} = 6 x - 18

- 3 r < 33

4 - 2 x < 3 x + 1 \leq 7

- 3 x^{2} + 12 x + 1 = 0

- 2.6 r = 2.08

What is ((5x^6y^2)/(10x^4y))^2 ?
The solution to ((5x^6y^2)/(10x^4y))^2 is (x^4y^2)/4