What is ((5a^2b)/(2a^3b))^2 ?

The solution to ((5a^2b)/(2a^3b))^2 is (25)/(4a^2)

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simplify ((5a^2b)/(2a^3b))^2

simplify

(\frac{5 a ^{2} b}{2 a ^{3} b})^{2}

\frac{25}{4 a ^{2}}

Solution steps

(\frac{5 a ^{2} b}{2 a ^{3} b})^{2}

Apply exponent rule:

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

= \frac{( 5 a ^{2} b ) ^{2}}{( 2 a ^{3} b ) ^{2}}

Simplify

(5 a^{2} b)^{2} : 25 a^{4} b^{2}

= \frac{25 a ^{4} b ^{2}}{( 2 a ^{3} b ) ^{2}}

Simplify

(2 a^{3} b)^{2} : 4 a^{6} b^{2}

= \frac{25 a ^{4} b ^{2}}{4 a ^{6} b ^{2}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{a ^{4}}{a ^{6}} = \frac{1}{a ^{6 - 4}}

= \frac{25 b ^{2}}{4 b ^{2} a ^{6 - 4}}

Subtract the numbers:

6 - 4 = 2

= \frac{25 b ^{2}}{4 a ^{2} b ^{2}}

Cancel the common factor:

b^{2}

= \frac{25}{4 a ^{2}}

(- 2) \cdot (- 3)

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

(64)^{- \frac{1}{3}}

(x + 5) (x - 5) (x^{2} + 1)

What is ((5a^2b)/(2a^3b))^2 ?
The solution to ((5a^2b)/(2a^3b))^2 is (25)/(4a^2)