Question

write \\((2p^2)^3\\) without exponents.

\\((2p^2)^3 = \square\\)

fill in the blanks.

\\((2p^2)^3 = \square p^{\square}\\)

Explanation:

Apply the power of a product rule

We distribute the outer exponent to each factor inside the parentheses.

$$ (2p^2)^3 = 2^3 \cdot (p^2)^3 $$

Simplify the numerical coefficient

We calculate the value of the base raised to the power.

$$ 2^3 = 2 \cdot 2 \cdot 2 = 8 $$

Apply the power of a power rule

We multiply the exponents for the variable base.

$$ (p^2)^3 = p^{2 \cdot 3} = p^6 $$

Combine the simplified terms

We write the final simplified expression.

$$ (2p^2)^3 = 8p^6 $$

Expand the expression without exponents

We write out the repeated multiplication to show the expression without exponents.

$$ (2p^2)^3 = (2p^2) \cdot (2p^2) \cdot (2p^2) = 2 \cdot p \cdot p \cdot 2 \cdot p \cdot p \cdot 2 \cdot p \cdot p = 8pppppp $$

Answer:

Question 1

Write \((2p^2)^3\) without exponents.
\((2p^2)^3 =\) <blank>\(8pppppp\)</blank>

Question 2

Fill in the blanks.
\((2p^2)^3 =\) <blank>\(8\)</blank>\(p\)<blank>\(6\)</blank>