Solve: 8⁷ × 10⁷ × 16⁷ Power Multiplication Problem

The given expression is $8^7\times10^7\times16^7$. We need to apply the power of a product rule for exponents. This rule states that for any numbers $a$, $b$, and $c$, if they have the same exponent $n$, then $a^n \times b^n \times c^n = (a\times b \times c)^n$.

In this problem, we recognize that 8, 10, and 16 all have the same exponent of 7, thus, we can apply the rule directly:

• $8^7 \times 10^7 \times 16^7$
• Applying the power of a product rule:
• $(8 \times 10 \times 16)^7$

This simplified form matches the pattern we recognize from the power of a product rule, verifying that $(8\times10\times16)^7$ is indeed the correct transformation of the original expression $8^7\times10^7\times16^7$, thereby confirming our answer is correct.