Question: The simplified form of $3^7 \times 3^5 \times 3^1$ expressed as a power is - $3^{13}$ - $3^{12}$…

The simplified form of $3^7 \times 3^5 \times 3^1$ expressed as a power is

• $3^{13}$
• $3^{12}$
• $27^{15}$
• $3^{35}$

Solution

The problem asks for the simplified form of the expression \(3^7 \times 3^5 \times 3^1\) expressed as a power. To simplify this, we use the rule of exponents that states \(a^m \times a^n = a^{m+n}\). First, identify the base, which is \(3\), and add the exponents: \[ 3^7 \times 3^5 \times 3^1 = 3^{7+5+1} \] Simplify the exponent: \[ 3^{7+5+1} = 3^{13} \] So, the simplified form of \(3^7 \times 3^5 \times 3^1\) is \(3^{13}\).