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 $(a\times b\times c)^n=a^n\times b^n\times c^n$.

In this problem, we recognize that 8, 10, and 16 all have the same exponent of 7. Therefore 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 $8^7\times10^7\times16^7$.