Question 32

5^4 * 2^13

The expression simplifies to 5^4 * 2^13, making this the correct option. This result is derived from applying the laws of exponents correctly to the given expression.

A) 5^3 * 2^11

This option is incorrect as it does not account for the full simplification of the powers of 5 and 2 in the expression. Following the exponent rules would yield higher exponents than those presented in this choice.

B) 5^(-12) * 2^40

This option is also incorrect. The negative exponent for 5 suggests a miscalculation in the simplification process, and the exponent for 2 is much too high compared to the actual calculations from the original expression.

C) 5^4 * 2^13

This option is correct as it accurately represents the result of simplifying the original expression. By applying the exponent rules, we find that the multiplication leads to these specific powers.

D) (-5)^8 * 2^13

This option is incorrect because it introduces a negative base for the power of 5, which is not present in the original expression. The correct simplification does not involve negative bases, and the exponent for 5 should remain positive.

Conclusion

The correct answer, 5^4 * 2^13, is derived from proper application of exponent rules to the original expression. All other options fail to represent the accurate simplification, either by presenting incorrect exponents or introducing unnecessary negative bases. Thus, C stands out as the definitive correct choice.