Question

consider the power $3^4$. which are correct descriptions of this power? check all that apply. ☐ the power is the product of 3 and 4. ☐ the power is described as 3 to the fourth power. ☐ the power means 3 factors of 4 are being multiplied. ☐ the power can be expanded as $3 \cdot 3 \cdot 3 \cdot 3$. ☐ the value of this power is 81.

Explanation:

• For the first option: The product of 3 and 4 is \( 3 \times 4 = 12 \), but \( 3^4 \) is not a product of 3 and 4 (it is a product of four 3s), so this is incorrect.
• For the second option: By definition, \( a^n \) is read as "a to the nth power", so \( 3^4 \) is "3 to the fourth power"—this is correct.
• For the third option: \( 3^4 \) means 4 factors of 3 (not 3 factors of 4) are multiplied, so this is incorrect.
• For the fourth option: Exponential form \( a^n \) expands to \( a \cdot a \cdot \dots \cdot a \) (n times), so \( 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 \)—this is correct.
• For the fifth option: Calculating \( 3 \cdot 3 \cdot 3 \cdot 3 = 81 \), so the value of \( 3^4 \) is 81—this is correct.

Answer:

B. The power is described as 3 to the fourth power.
D. The power can be expanded as \( 3 \cdot 3 \cdot 3 \cdot 3 \).
E. The value of this power is 81.