Step 1a

Given expression \$2^3 \times 2^2\$.

Apply the product rule for exponents: \$(a^m \times a^n) = a^(m+n)\$

\$2^3 \times 2^2 = 2^(3+2)\$

Explanation: Here, we applied the product rule.

Step 1b

Add the exponents:

\$2^3 \times 2^2 = 2^5\$

So, the expression \$2^3 \times 2^2\$ simplifies to \$2^5\$.

Explanation: Here, we added the exponents we get \$ 2^5 \$.

Step 2a

Given expression \$ 6^7/ 6^3 \$.

Apply the quotient rule for exponents: \$(a^m / a^n) = a^(m-n)\$

\$ 6^7 / 6^3 = 6^(7-3) \$

Explanation: Here, we applied the quotient rule.

Step 2b

Subtract the exponents:

\$6^7/6^3 = 6^4\$

The solved expression is \$6^4\$.

Explanation: So, the expression \$6^7/6^3\$ simplifies to \$6^4\$.