Question

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which expression is equivalent to $2^2 \times 3^2$?\
a $5^4$\
b $6^2$\
c $5^2$\
d $6^4$

Explanation:

Step1: Recall the exponent rule

We know the rule \((ab)^n = a^n\times b^n\) (reverse of the distributive property of exponents). Here we have \(2^{2}\times3^{2}\), and we can apply the formula \((ab)^n=a^n\times b^n\) in reverse. So \(2^{2}\times3^{2}=(2\times3)^{2}\)

Step2: Calculate \(2\times3\)

Calculate \(2\times3 = 6\), so \((2\times3)^{2}=6^{2}\)

Step3: Verify other options (optional but for clarity)

• Option A: \(5^{4}=5\times5\times5\times5 = 625\), and \(2^{2}\times3^{2}=4\times9 = 36\), \(625

eq36\)

• Option C: \(5^{2}=25

eq36\)

• Option D: \(6^{4}=6\times6\times6\times6=1296

eq36\)

Answer:

B. \(6^2\)