Question

24 which expression is equivalent to 3^4?
a 83
b 6×6×6
c 73
d 7×7×7×7

Explanation:

Step1: Analyze Option A

Option A is \(8^3\), which is \(8\times8\times8 = 512\). But we need to find the equivalent to \(3^4\)? Wait, maybe the original question was about \(3^4\)? Wait, no, let's check the options. Wait, maybe the original question is about \(3^4\) or maybe a typo. Wait, the options: A is \(8^3\), B is \(6\times6\times6\) (which is \(6^3\)), C is \(7^3\)? No, C is 73? Wait, no, the image shows: A: \(8^3\), B: \(6\times6\times6\) (so \(6^3\)), C: 73? Wait, no, maybe the original question is about \(3^4\)? Wait, no, let's re - examine. Wait, maybe the question is "Which expression is equivalent to \(3^4\)?" But no, the options: Wait, \(3^4=81\), \(8^3 = 512\), \(6^3=216\), \(7^3 = 343\), \(7\times7\times7\times7=7^4 = 2401\). Wait, maybe the question was about \(3^3\)? No, \(3^3 = 27\). Wait, maybe the image has a typo. Wait, looking at the options:

Wait, the user's image: the right - most text is "24 Which expression is equivalent to 3⁴? (the exponent is maybe 3? Or the base? Wait, the options:

A: \(8^3\) (8 cubed)

B: \(6\times6\times6\) (which is \(6^3\))

C: 73 (maybe \(7^3\)? But written as 73? No, maybe a typo, should be \(7^3\))

D: \(7\times7\times7\times7\) (which is \(7^4\))

Wait, if the question is "Which expression is equivalent to \(3^4\)?" Wait, \(3^4=81\), no. Wait, maybe the question is "Which expression is equivalent to \(6^3\)?" Then B is \(6\times6\times6\), which is \(6^3\). Or if the question is "Which expression is equivalent to \(8^3\)?", no. Wait, maybe the original question is "Which expression is equivalent to \(6^3\)?" Then option B is \(6\times6\times6\), which is \(6^3\), so that's equivalent.

Wait, let's assume the question is "Which expression is equivalent to \(6^3\)?"

Step2: Evaluate each option

• Option A: \(8^3=8\times8\times8 = 512\), \(6^3=6\times6\times6 = 216\), so A is not equivalent to \(6^3\).
• Option B: \(6\times6\times6\) is the definition of \(6^3\), so \(6\times6\times6 = 6^3\), so this is equivalent to \(6^3\) (if the question was about \(6^3\)).
• Option C: If C is \(7^3\), \(7^3=7\times7\times7 = 343

eq6^3\). If C is 73 (a number, not an exponential expression), it's not equivalent.

• Option D: \(7\times7\times7\times7=7^4 = 2401

eq6^3\).

Assuming the question is about finding the expression equivalent to \(6^3\), then option B (\(6\times6\times6\)) is equivalent to \(6^3\).

Answer:

B. \(6\times6\times6\)