Which of the following is equivalent to the expression below? 7^8.27 A. 7^8 7^2/10 7^7/100 B. 7^6 7^2/10 7^7/100 C. 7^8 * 7^27/100 D. 7^8 + 7^2/10 + 7^7/100

Answer: C. \( 7^6 \times 7^{27/100} \)

Explanation: The expression \( 7^{6.27} \) can be rewritten using the properties of exponents. Specifically, we use the rule that \( a^{m+n} = a^m \times a^n \). Here, we split the exponent \( 6.27 \) into \( 6 + 0.27 \).

Steps:

1. Identify the Expression:

1. Split the Exponent:

• \( 6.27 = 6 + 0.27 \)

1. Apply the Exponent Rule:

1. Convert Decimal to Fraction:

• \( 0.27 = \frac{27}{100} \)

1. Rewrite the Expression:

Thus, the equivalent expression is \( 7^6 \times 7^{27/100} \), which corresponds to option C.