What is ((4ab^2)/(5ab))^2 ?

The solution to ((4ab^2)/(5ab))^2 is (16b^2)/(25)

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simplify ((4ab^2)/(5ab))^2

simplify

(\frac{4 a b ^{2}}{5 ab})^{2}

\frac{16 b ^{2}}{25}

Solution steps

(\frac{4 a b ^{2}}{5 ab})^{2}

Apply exponent rule:

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

= \frac{( 4 a b ^{2} ) ^{2}}{( 5 ab ) ^{2}}

Simplify

(4 a b^{2})^{2} : 16 a^{2} b^{4}

= \frac{16 a ^{2} b ^{4}}{( 5 ab ) ^{2}}

Simplify

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

= \frac{16 a ^{2} b ^{4}}{25 a ^{2} b ^{2}}

Cancel the common factor:

a^{2}

= \frac{16 b ^{4}}{25 b ^{2}}

Apply exponent rule:

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

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

= \frac{16 b ^{4 - 2}}{25}

Subtract the numbers:

4 - 2 = 2

= \frac{16 b ^{2}}{25}

\frac{- 2}{- 8}

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\frac{2 π}{( \frac{π}{2} )}

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2 x^{2} + 7 = 0