Question

Which applies the power of a product rule to simplify (5^7) * (5^3)?

A) (5^0) = 5
B) (5^1) * 9 = 3(5^1) = 15
C) (5^0) * 5^7 - 5^13
D) (5^0) = 5^4 = 125

Answer 1

The correct application of the power of a product rule to simplify (5^7) * (5^3) is D) (5^7) * (5^3) = 5^(7+3) = 5^10 = 9765625.

Step-by-step explanation:

When simplifying expressions with the same base raised to different exponents and multiplied together, you can apply the power of a product rule. This rule states that when multiplying two powers with the same base, you add their exponents together.

For the expression (5^7) * (5^3), both terms have the base 5. According to the power of a product rule, when multiplying powers with the same base, you add their exponents. In this case, the exponents are 7 and 3. So, (5^7) * (5^3) = 5^(7+3) = 5^10.

Solving the exponent 5^10 gives the result of 9765625. Therefore, the correct application of the power of a product rule simplifies (5^7) * (5^3) to 5^10, which equals 9765625. This demonstrates the fundamental rule of combining exponents with the same base when multiplying terms together.