Question

which prime facorization does not correctly represent the number shown? 48 = 2⁴·3 100 = 2³·5² 144 = 2⁴·3² clear my selection 5 multiple choice 1 point which expression is equivalent to 52·52·52·52 4⁵² 5⁴ + 2⁴ 52⁴ 52 clear my selection

Explanation:

Step1: Verify first prime factorization

Calculate $2^4 \cdot 3 = 16 \cdot 3 = 48$, which matches.

Step2: Verify second prime factorization

Calculate $2^3 \cdot 5^2 = 8 \cdot 25 = 200$, which does not equal 100.

Step3: Verify third prime factorization

Calculate $2^4 \cdot 3^2 = 16 \cdot 9 = 144$, which matches.

Step4: Rewrite repeated multiplication as exponent

$52 \cdot 52 \cdot 52 \cdot 52$ is 52 multiplied 4 times, so it equals $52^4$.

Answer:

1. $100 = 2^3 \cdot 5^2$
2. $52^4$