Logarithm and A...

Simplify:
$$\left( { 4 }^{ -1 }\times { 3 }^{ -1 } \right) \div { 6 }^{ -1 }$$

Simplify and give reasons:
$${(-2)}^{7}$$

Simplify the following:
$${ (-2) }^{ 7 }\times { (-2) }^{ 3 }\times { (-2) }^{ 4 }$$

Simplify and give reasons:
$$\cfrac { { 3 }^{ -2 } }{ 3 } \times \left( { 3 }^{ 0 }-{ 3 }^{ -1 } \right) $$

Simplify the following:
$${ \left( \cfrac { 1 }{ 2 }  \right)  }^{ 4 }\times { \left( \cfrac { 1 }{ 2 }  \right)  }^{ 5 }\times { \left( \cfrac { 1 }{ 2 }  \right)  }^{ 6 }$$

Simplify and give reasons:
$$\left[ { \left( \cfrac { 3 }{ 2 }  \right)  }^{ -2 } \right] ^{ 2 }$$

Simplify and give reasons:
$${(-3)}^{-4}$$

Simplify:
$$\left[ { \left( \cfrac { 3 }{ 5 }  \right)  }^{ -2 }\div { \left( \cfrac { 4 }{ 5 }  \right)  }^{ -3 } \right] \times { { \left( \cfrac { 3 }{ 5 }  \right)  } }^{ -2 }$$

Exponential form of $$\log_{4}8 = x$$ is _____

The logarithmic form of $${5}^{2}=25$$ is