Calculate 7^9 × 7: Solving a Power Multiplication Problem

Any number without a visible exponent actually has an invisible exponent of 1. So 7 = $7^1$, just like how 5 = $5^1$. This is why $7^9 \times 7 = 7^9 \times 7^1$.

The exponent addition rule only works with the same base! For example, $7^2 \times 3^2$ cannot be simplified using this rule. You'd need to calculate each power separately first.

Add exponents when multiplying same bases: $a^m \times a^n = a^{m+n}$
Multiply exponents when raising a power to a power: $(a^m)^n = a^{m \times n}$

You could calculate $7^9 = 40,353,607$ then multiply by 7, but that's much harder! Using the exponent rule gives you $7^{10}$ instantly and keeps your answer in the simplest form.

$7^{10}$ means 7 multiplied by itself 10 times, while $14^9$ means 14 multiplied by itself 9 times. These are completely different values - never add the bases when using exponent rules!