What is ((a/b)^2)^5((a^3b^2)/(c^3))^{3^'} ?

The solution to ((a/b)^2)^5((a^3b^2)/(c^3))^{3^'} is (a^{10+3^{'+1}}b^{2*3^'-10})/(c^{3^{'+1)}}

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simplify ((a/b)^2)^5((a^3b^2)/(c^3))^{3^'}

simplify

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

\frac{a ^{10 + 3^{' + 1}} b ^{2 \cdot 3^{'} - 10}}{c ^{3^{' + 1}}}

Solution steps

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

((\frac{a}{b})^{2})^{5} : (\frac{a}{b})^{10}

= (\frac{a}{b})^{10} (\frac{a ^{3} b ^{2}}{c ^{3}})^{3^{^{^{'}}}}

(\frac{a}{b})^{10} = \frac{a ^{10}}{b ^{10}}

= \frac{a ^{10}}{b ^{10}} (\frac{a ^{3} b ^{2}}{c ^{3}})^{3^{^{^{'}}}}

Multiply fractions:

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

= \frac{a ^{10} ( \frac{a ^{3} b ^{2}}{c ^{3}} ) ^{3^{^{^{'}}}}}{b ^{10}}

(\frac{a ^{3} b ^{2}}{c ^{3}})^{3^{^{'}}} = \frac{( a ^{3} b ^{2} ) ^{3^{^{'}}}}{c ^{3^{1 +^{'}}}}

= \frac{\frac{( a ^{3} b ^{2} ) ^{3^{^{^{'}}}}}{c ^{3^{^{^{'}} + 1}}} a ^{10}}{b ^{10}}

Multiply

a^{10} \frac{( a ^{3} b ^{2} ) ^{3^{^{'}}}}{c ^{3^{1 +^{'}}}} : \frac{a ^{10 + 3^{^{'} + 1}} b ^{2 \cdot 3^{^{'}}}}{c ^{3^{1 +^{'}}}}

= \frac{\frac{a ^{10 + 3^{^{'} + 1}} b ^{2 \cdot 3^{^{'}}}}{c ^{3^{1 +^{'}}}}}{b ^{10}}

Apply the fraction rule:

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

= \frac{b ^{2 \cdot 3^{^{^{'}}}} a ^{3^{1 +^{^{'}}} + 10}}{c ^{3^{1 +^{^{'}}}} b ^{10}}

Apply exponent rule:

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

\frac{b ^{2 \cdot 3^{^{'}}}}{b ^{10}} = b^{2 \cdot 3^{^{'}} - 10}

= \frac{a ^{10 + 3^{^{^{'}} + 1}} b ^{2 \cdot 3^{^{^{'}}} - 10}}{c ^{3^{1 +^{^{'}}}}}

(5 x^{2} y) (3 x y^{5})

e^{- k \cdot 0}

9.7 \cdot 1 0^{- 7}

3 t \cdot e^{- 2 t} \cdot cos (4 t)

2 \cdot 1 0^{- 7} \cdot \frac{4.5}{16 \cdot 1 0 ^{- 2}}

What is ((a/b)^2)^5((a^3b^2)/(c^3))^{3^'} ?
The solution to ((a/b)^2)^5((a^3b^2)/(c^3))^{3^'} is (a^{10+3^{'+1}}b^{2*3^'-10})/(c^{3^{'+1)}}