What is ((a^4b^2)/(a^{-3)b^9})^4 ?

The solution to ((a^4b^2)/(a^{-3)b^9})^4 is (a^{28})/(b^{28)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((a^4b^2)/(a^{-3)b^9})^4

simplify

(\frac{a ^{4} b ^{2}}{a ^{- 3} b ^{9}})^{4}

\frac{a ^{28}}{b ^{28}}

Solution steps

(\frac{a ^{4} b ^{2}}{a ^{- 3} b ^{9}})^{4}

Apply exponent rule:

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

= \frac{( a ^{4} b ^{2} ) ^{4}}{( a ^{- 3} b ^{9} ) ^{4}}

Simplify

(a^{4} b^{2})^{4} : a^{16} b^{8}

= \frac{a ^{16} b ^{8}}{( a ^{- 3} b ^{9} ) ^{4}}

Simplify

(a^{- 3} b^{9})^{4} : \frac{b ^{36}}{a ^{12}}

= \frac{a ^{16} b ^{8}}{\frac{b ^{36}}{a ^{12}}}

Apply the fraction rule:

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

= \frac{a ^{16} b ^{8} a ^{12}}{b ^{36}}

Apply exponent rule:

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

\frac{b ^{8}}{b ^{36}} = \frac{1}{b ^{36 - 8}}

= \frac{a ^{16} a ^{12}}{b ^{36 - 8}}

Subtract the numbers:

36 - 8 = 28

= \frac{a ^{16} a ^{12}}{b ^{28}}

a^{16} a^{12} = a^{28}

= \frac{a ^{28}}{b ^{28}}

\frac{1}{u} + \frac{1}{v}

\frac{( 3 x + 4 )}{2} - \frac{( 5 x - 2 )}{3}

\frac{( 5 ^{2 (n + 6)} \cdot ( 25 ) ^{- 7 + 2 n} )}{( ( 125 ) ^{2 n} )}

- 1.6 (a + b + c) - 3.2 (2.7 a - c) + 4.3 (a + 2.5 b)

- x^{4} \cdot y^{10}

What is ((a^4b^2)/(a^{-3)b^9})^4 ?
The solution to ((a^4b^2)/(a^{-3)b^9})^4 is (a^{28})/(b^{28)}