Calculate: b \times (2b^3)^{-3}

Expression: $b \times {\left( 2{b}^{3} \right)}^{-3}$

To raise a product to a power, raise each factor to that power

$b \times {2}^{-3}{b}^{-9}$

Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$

$b \times \frac{ 1 }{ {2}^{3} } \times {b}^{-9}$

Evaluate the power

$b \times \frac{ 1 }{ 8 }{b}^{-9}$

Calculate the product

$\frac{ 1 }{ 8 }{b}^{-8}$

Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$

$\frac{ 1 }{ 8 } \times \frac{ 1 }{ {b}^{8} }$

Multiply the fractions

$\frac{ 1 }{ 8{b}^{8} }$