Question

follow the instructions below.
write (left(4y^{4}
ight)^{2}) without exponents.
(left(4y^{4}
ight)^{2}=square)
fill in the blanks.
(left(4y^{4}
ight)^{2}=16y^{8})

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((4y^4)^2\), we apply this rule: \(4^2\times(y^4)^2\).

Step2: Calculate the powers

First, calculate \(4^2\), which is \(4\times4 = 16\). Then, use the power of a power rule \((a^m)^n=a^{m\times n}\) for \((y^4)^2\), so \(y^{4\times2}=y^8\).

Step3: Combine the results

Multiply the two results together: \(16\times y^8 = 16y^8\). To write it without exponents (expanded form for the variable part, but since \(y^8\) is \(y\times y\times y\times y\times y\times y\times y\times y\)), we have \(16\times y\times y\times y\times y\times y\times y\times y\times y\), which is \(16yyyyyyyy\) (but usually, we keep the coefficient and the variable with exponent or expand the variable part. However, since \(y^8\) expanded is \(y\) multiplied by itself 8 times, the full expanded form without exponents for \((4y^4)^2\) is \(4\times4\times y\times y\times y\times y\times y\times y\times y\times y\) which simplifies to \(16yyyyyyyy\) or \(16y^8\) (but the problem says "without exponents" for the expression, so we expand the variable part: \(4\times4\times y\times y\times y\times y\times y\times y\times y\times y = 16\times y\times y\times y\times y\times y\times y\times y\times y\)).

Answer:

\(16\times y\times y\times y\times y\times y\times y\times y\times y\) (or \(16yyyyyyyy\))