Question

Write your answer as a power or as a product of powers. $$ \left[(5+x)^{3}\right]^{6} $$

Short answer

The simplified expression is \((5 + x)^{18}\)

Step-by-step solution

Identify the base and the exponents

The base in this problem is \((5+x)\) and the two exponents are 3 and 6.

Apply the power of a power rule

The power of a power rule states that \((a^n)^m\) can be simplified as \(a^{n \times m}\). Applying this rule to our expression gives \((5 + x)^{3 \times 6}\).

Multiply the exponents

Multiply 3 by 6 to obtain the final exponent. This gives \((5 + x)^{18}\).