Question

Simplify. $$ \left(8 x^{2} y^{8}\right)^{3} $$

Short answer

The simplified form of the given expression is \(512 x^{6} y^{24}\)

Step-by-step solution

Step 1:Apply the exponent to each part inside the parentheses

Apply the exponent of 3 to each part inside the parentheses independently. It gives us: \(8^{3} (x^{2})^{3} (y^{8})^{3}\).

Simplify the exponential terms

Now, simplify each exponential term. As per the rules of exponents, when raising a power to a power, you multiply the exponents. \(8^{3}\) gives \(512\), \((x^{2})^{3}\) simplifies to \(x^{6}\), and \((y^{8})^{3}\) simplifies to \(y^{24}\).

Combine all the terms

After simplifying the terms, combine them all in one expression: \(512 x^{6} y^{24}\).