5 ^ 3.5 * 5 ^ 4.5 * 5 ^ 2.4 / (5 ^ - 7) =\$^ 51

Let's solve the given expression step by step:

The expression is:

\[
5^{3.5} \times 5^{4.5} \times 5^{2.4} \div 5^{-7} = 5^{51}
\]

We'll use the properties of exponents to simplify:

1. When multiplying powers with the same base, add their exponents:
   \[
   5^{3.5} \times 5^{4.5} \times 5^{2.4} = 5^{(3.5 + 4.5 + 2.4)} = 5^{10.4}
   \]

2. When dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator:
   \[
   \frac{5^{10.4}}{5^{-7}} = 5^{10.4 - (-7)} = 5^{10.4 + 7} = 5^{17.4}
   \]

So the expression simplifies to:

\[
5^{17.4} = 5^{51}
\]

Since $5^{17.4} \neq 5^{51}$, the equation cannot be true. Thus, there must be a mistake in the problem's equality statement.

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Explore how to solve the exponential equation 5^3.5 * 5^4.5 * 5^2.4 / (5^-7) = 5^51 step-by-step. This problem involves properties of exponents and requires understanding of exponent rules. Suitable for students in Grades 9-12.

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