Question

Simplify. (2u^(4)w^(3))^(5) Write your answer witho

Answer 1

The expression
`\((2u^4w^3)^5\)` simplifies to
`\(32u^(20)w^(15)\)` using the power of a power rule. Applying the rule involves multiplying the exponents, resulting in the concise and simplified form.

Step-by-step explanation:

In the given expression
`\((2u^4w^3)^5\)`, we apply the power of a power rule, which states that when a power is raised to another power, you multiply the exponents. In this case, we multiply the exponents of (u) and (w) by 5. Thus,
`\((2u^4w^3)^5 = 2^5u^(4 * 5)w^(3 * 5)\).`

Now, simplify the exponents further.
`\(2^5 = 32\), \(4 * 5 = 20\), and \(3 * 5 = 15\). Therefore, the simplified expression is \(32u^(20)w^(15)\).`

This result represents the fifth power of the original expression, meaning we have five identical factors of
`\((2u^4w^3)\)` multiplied together. Each factor contributes its own set of powers of (u) and (w), and when combined, the exponents add up to give the final result.

In conclusion, the expression
`\((2u^4w^3)^5\)`simplifies to
`\(32u^(20)w^(15)\)`by applying the power of a power rule and performing the necessary exponent operations. This concise form is obtained by efficiently combining the repeated factors, showcasing the fundamental rules of exponentiation.