Power Rule of Exponents Quick Check 3 of 5

Question

If the expression was
simplified using the Power
Rule of Exponents, what is an
equivalent expanded
expression? (1 point)
4
10
(4 )
2
8
4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4
(4 )
5
2
(4 )
12
2

Answer 1

To determine the equivalent expanded expression, we first need to apply the Power Rule of Exponents correctly:

The Power Rule states that \( (a^m)^n = a^{m \cdot n} \).

Let's analyze the expressions provided:

1. \( (4^2)^8 \) - According to the Power Rule, this simplifies to \( 4^{2 \cdot 8} = 4^{16} \).
2. \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \) - This is \( 4^7 \), since it is multiplying 4 a total of 7 times.
3. \( (4^5)^2 \) - This simplifies to \( 4^{5 \cdot 2} = 4^{10} \).
4. \( (4^{12})^2 \) - This simplifies to \( 4^{12 \cdot 2} = 4^{24} \).

From the original information, we can discern the expanded forms:

• For \( 4^{16} \): \( 4 \) appears 16 times: \( 4 \times 4 \times 4 \times \ldots \) (16 times)
• For \( 4^7 \): \( 4 \) appears 7 times: \( 4 \times 4 \times \ldots \) (7 times)
• For \( 4^{10} \): \( 4 \) appears 10 times: \( 4 \times 4 \times \ldots \) (10 times)
• For \( 4^{24} \): \( 4 \) appears 24 times: \( 4 \times 4 \times \ldots \) (24 times)

Please clarify which specific expression you are referring to, or if you would like to see the expanded version of a specific exponentiation.