Simplify 2⁹ × 4⁹ × 7⁹: Product of Powers Expression

The given expression is $2^9 \times 4^9 \times 7^9$.

We need to simplify this expression by using the exponent rule for the power of a product. The rule states that $(a \times b \times c)^n = a^n \times b^n \times c^n$, which can be inverted to simplify a product of terms with the same exponent.

Thus, the expression $2^9 \times 4^9 \times 7^9$ can be rewritten as $(2 \times 4 \times 7)^9$.

Breaking it down:

• Identify the common exponent, which is $9$.

• Combine the bases under a single power:

  • The bases are $2, 4,$ and $7$.

• Apply the exponent rule: $2^9 \times 4^9 \times 7^9 = (2 \times 4 \times 7)^9$.

Therefore, the corresponding expression is $\left(2\times4\times7\right)^9$.