What is (3/5)^7left(15/12)^7left(2/7)^3 ?

The solution to (3/5)^7left(15/12)^7left(2/7)^3 is (2187e^2l^2f^2t^2)/(702464)

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simplify (3/5)^7left(15/12)^7left(2/7)^3

simplify

(\frac{3}{5})^{7} l e f t (\frac{15}{12})^{7} l e f t (\frac{2}{7})^{3}

\frac{2187 e ^{2} l ^{2} f ^{2} t ^{2}}{702464}

Solution steps

(\frac{3}{5})^{7} l e f t (\frac{15}{12})^{7} l e f t (\frac{2}{7})^{3}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

ll = l^{1 + 1}

= (\frac{3}{5})^{7} e f t (\frac{15}{12})^{7} l^{1 + 1} e f t (\frac{2}{7})^{3}

Add the numbers:

1 + 1 = 2

= (\frac{3}{5})^{7} e f t (\frac{15}{12})^{7} l^{2} e f t (\frac{2}{7})^{3}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

ee = e^{1 + 1}

= (\frac{3}{5})^{7} f t (\frac{15}{12})^{7} l^{2} e^{1 + 1} f t (\frac{2}{7})^{3}

Add the numbers:

1 + 1 = 2

= (\frac{3}{5})^{7} f t (\frac{15}{12})^{7} l^{2} e^{2} f t (\frac{2}{7})^{3}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

ff = f^{1 + 1}

= (\frac{3}{5})^{7} t (\frac{15}{12})^{7} l^{2} e^{2} f^{1 + 1} t (\frac{2}{7})^{3}

Add the numbers:

1 + 1 = 2

= (\frac{3}{5})^{7} t (\frac{15}{12})^{7} l^{2} e^{2} f^{2} t (\frac{2}{7})^{3}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

tt = t^{1 + 1}

= (\frac{3}{5})^{7} (\frac{15}{12})^{7} l^{2} e^{2} f^{2} t^{1 + 1} (\frac{2}{7})^{3}

Add the numbers:

1 + 1 = 2

= (\frac{3}{5})^{7} (\frac{15}{12})^{7} l^{2} e^{2} f^{2} t^{2} (\frac{2}{7})^{3}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

(\frac{3}{5})^{7} (\frac{15}{12})^{7} = (\frac{3}{5} \cdot \frac{15}{12})^{7}

= e^{2} (\frac{2}{7})^{3} (\frac{3}{5} \cdot \frac{15}{12})^{7} l^{2} f^{2} t^{2}

\frac{3}{5} \cdot \frac{15}{12} = \frac{3}{4}

= e^{2} (\frac{3}{4})^{7} (\frac{2}{7})^{3} l^{2} f^{2} t^{2}

(\frac{3}{4})^{7} = \frac{3 ^{7}}{4 ^{7}}

= e^{2} (\frac{2}{7})^{3} \frac{3 ^{7}}{4 ^{7}} l^{2} f^{2} t^{2}

(\frac{2}{7})^{3} = \frac{2 ^{3}}{7 ^{3}}

= e^{2} \frac{3 ^{7}}{4 ^{7}} \cdot \frac{2 ^{3}}{7 ^{3}} l^{2} f^{2} t^{2}

Multiply fractions:

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

= \frac{3 ^{7} \cdot 2 ^{3} l ^{2} e ^{2} f ^{2} t ^{2}}{4 ^{7} \cdot 7 ^{3}}

Factor

4^{7} : 2^{14}

= \frac{3 ^{7} \cdot 2 ^{3} e ^{2} l ^{2} f ^{2} t ^{2}}{2 ^{14} \cdot 7 ^{3}}

Cancel

\frac{3 ^{7} \cdot 2 ^{3} l ^{2} e ^{2} f ^{2} t ^{2}}{2 ^{14} \cdot 7 ^{3}} : \frac{3 ^{7} e ^{2} l ^{2} f ^{2} t ^{2}}{2 ^{11} \cdot 7 ^{3}}

= \frac{3 ^{7} e ^{2} l ^{2} f ^{2} t ^{2}}{2 ^{11} \cdot 7 ^{3}}

3^{7} = 2187

= \frac{2187 e ^{2} l ^{2} f ^{2} t ^{2}}{2 ^{11} \cdot 7 ^{3}}

2^{11} \cdot 7^{3} = 702464

= \frac{2187 e ^{2} l ^{2} f ^{2} t ^{2}}{702464}

\frac{2 π}{5}

0.5 x^{- 0.5}

What is (3/5)^7left(15/12)^7left(2/7)^3 ?
The solution to (3/5)^7left(15/12)^7left(2/7)^3 is (2187e^2l^2f^2t^2)/(702464)