The expression \( \frac{7}{15} \) itself does not inherently involve exponents, but if we were to consider the exponentiation of the number 7, we can analyze the provided options in terms of exponents.
Let's break down the given options:
-
(7x7x7) x (7x7x7) x (7x7x7) x (7x7x7) x (7x7x7):
This expression represents \( 7^3 \times 7^3 \times 7^3 \times 7^3 \times 7^3 \).
Since there are 5 groups of \( 7^3 \), this simplifies to \( (7^3)^5 = 7^{15} \). -
(7 to the power of 10) to the power of 5:
This expression simplifies as follows: \( (7^{10})^5 = 7^{10 \times 5} = 7^{50} \). -
(7x7x7x7x7) to the power of 10:
This expression represents \( (7^5)^{10} = 7^{5 \times 10} = 7^{50} \). -
(7 to the power of 18) to the power of 3:
This expression simplifies as follows: \( (7^{18})^3 = 7^{18 \times 3} = 7^{54} \).
Among the provided options, the first one leads to \( 7^{15} \), while all others result in much larger powers of 7.
The expanded equivalent expression that matches the power rule in relation to having 7 in an exponent form is the first option:
Answer: (7x7x7) x (7x7x7) x (7x7x7) x (7x7x7) x (7x7x7) (This equals \( 7^{15} \)).