Evaluate the Expression: (4×10×7)^9 Step-by-Step

To solve the problem, we need to apply the power of a product rule of exponents. This rule states that $(a \times b \times c)^n = a^n \times b^n \times c^n$ for any numbers $a$, $b$, and $c$, and an exponent $n$.

Let's apply this rule to the given expression: $\left(4\times10\times7\right)^9$:

• Identify each factor inside the parentheses: 4, 10, and 7.

• The exponent applied is 9.

• Apply the rule: Each factor inside the parentheses is raised to the 9th power.

This gives us the expression: $4^9 \times 10^9 \times 7^9$.

Therefore, the final expression is: $4^9 \times 10^9 \times 7^9$