Question

what part of the expression $(5y)^3$ is raised to the third power?
$5y$
which expression shows $(5y)^3$ written without exponents?
$5y + 5y + 5y$ $15 \cdot y \cdot y$ $5y \cdot 5y \cdot 5y$ $15y$

Explanation:

Step1: Recall exponent definition

An exponent \(a^n\) means multiplying \(a\) by itself \(n\) times. For \((5y)^3\), the base is \(5y\) and the exponent is 3.

Step2: Apply exponent to base

So \((5y)^3\) is equivalent to multiplying \(5y\) three times: \(5y \cdot 5y \cdot 5y\).

Step3: Eliminate other options

• \(5y + 5y + 5y\) is addition, not exponentiation (exponentiation is repeated multiplication, not addition).
• \(15 \cdot y \cdot y\) incorrectly simplifies \(5y\) to 15 (we don't multiply 5 by 3 for the base; we multiply the base \(5y\) three times).
• \(15y\) is a simplified linear term, not the expanded form of \((5y)^3\).

Answer:

\(5y \cdot 5y \cdot 5y\)