Question

Simplify each expression.

${\left[{\left(2x{y}^3\right)}^2\right]}^{\mathbf{3}}$

Short answer

The required simplified value is represented by ${\mathbf{2}}^{\mathbf{6}}{\mathit{x}}^{\mathbf{6}}{\mathit{y}}^{\mathbf{18}}$

Step-by-step solution

Step 1. Write the variables with the both global exponents.

By using the global exponents 2 and 3, rewrite the provided expression.

$\begin{array}{c}{\left[2^2{x}^2{y}^{3\times 2}\right]}^3={\left[2^2{x}^2{y}^6\right]}^3\\ =\left[2^{2\times 3}{x}^{2\times 3}{y}^{6\times 3}\right]\end{array}$

Step 2. Simplify the exponential terms.

Perform multiplication between the exponents.

$2^6{x}^6{y}^{18}$

Step 3. Write the conclusion.

The obtained expression is$2^6{x}^6{y}^{18}$ which cannot be simplified further so it’s the required simplification.