Question

follow the instructions below.
write ((y^{2})^{3}) without exponents.
((y^{2})^{3}=)
fill in the blank.
((y^{2})^{3}=y^{square})

Explanation:

Part 1: Write \((y^2)^3\) without exponents

Step 1: Recall exponent rule

The power of a power rule states that \((a^m)^n = a^{m\times n}\), but to write without exponents, we expand \((y^2)^3\) as multiplying \(y^2\) three times. So \((y^2)^3=y^2\times y^2\times y^2\).

Step 2: Expand \(y^2\)

Since \(y^2 = y\times y\), substitute each \(y^2\):
\(y^2\times y^2\times y^2=(y\times y)\times(y\times y)\times(y\times y)\)

Step 3: Multiply the \(y\) terms

Multiply all the \(y\)s together: \(y\times y\times y\times y\times y\times y\)

Part 2: Fill in the blank \((y^2)^3 = y^{\square}\)

Step 1: Apply power of a power rule

The power of a power rule is \((a^m)^n=a^{m\times n}\). For \((y^2)^3\), \(a = y\), \(m = 2\), \(n=3\).

Step 2: Calculate the exponent

Multiply the exponents: \(2\times3 = 6\). So \((y^2)^3=y^6\).

Answer:

s:

• Without exponents: \(y\times y\times y\times y\times y\times y\)
• Blank: \(6\) (so \((y^2)^3 = y^{\boldsymbol{6}}\))