Final answer:
The product of five cubed (5³) and five to the fourth power (5⁴) is obtained by adding the exponents when the bases are the same, resulting in 5⁷, so the answer is (A) 5⁷.
Step-by-step explanation:
The product of five cubed (5³) and five to the fourth power (5⁴) is found by multiplying the two expressions. According to the rules for multiplying exponential numbers with the same base, we can simply add the exponents. Therefore, 5³ multiplied by 5⁴ equals 5³⁴. Each exponent indicates how many times the base number is multiplied by itself, so in this case, we need to add the number of times:
5³ = 5 × 5 × 5
5⁴ = 5 × 5 × 5 × 5
5³ × 5⁴ = (5 × 5 × 5) × (5 × 5 × 5 × 5) = 5·
Thus, when we multiply 5³ by 5⁴, we simply add the exponents 3 and 4 together, which gives us an exponent of 7. So, the correct answer is (A) 5⁷.