Multiplication of Powers Practice Problems & Solutions

To simplify the equation $12 \times 12^2$, follow these steps:

• Step 1: Recognize that 12 can be expressed as a power. Since $12 = 12^1$, rewrite the equation as $12^1 \times 12^2$.
• Step 2: Apply the rule for multiplying powers with the same base, which states that $a^m \times a^n = a^{m+n}$. In this case, this becomes $12^{1+2}$.
• Step 3: Simplify the expression by adding the exponents: $1 + 2 = 3$.

Thus, the simplified form of the expression is $12^3$.

Therefore, the correct answer choice is $12^{1+2}$, which corresponds to choice 2.

To simplify the expression given, $6^2 \times 6^8$, we will use the property of exponents which states that the product of two powers with the same base is the base raised to the sum of the exponents.

Let's apply the rule:

• The base in both powers is $6$.

• The exponents are $2$ and $8$.

• According to the rule $a^m \times a^n = a^{m+n}$, we add the exponents; therefore, $6^2 \times 6^8 = 6^{2+8}$.

• Simplifying further, this becomes $6^{10}$.

Therefore, the simplified expression is $6^{10}$.

The solution to the given problem is $6^{2+8}$.

To simplify the expression $2^2 \times 2^3$, we apply the rule for multiplying powers with the same base. According to this rule, when multiplying two exponential expressions that have the same base, we keep the base and add the exponents.

• Step 1: Identify the base: In this problem, the base for both terms is 2.
• Step 2: Apply the exponent multiplication rule: $2^2 \times 2^3 = 2^{2+3}$.
• Step 3: Simplify by adding the exponents: $2^{2+3} = 2^5$.

Thus, the simplified form of the expression $2^2 \times 2^3$ is $2^{5}$.

The correct choice from the provided options is: $2^{2+3}$.

To simplify the expression $4^5 \times 4^5$, we will use the rule of exponents that states when multiplying two powers with the same base, you can add the exponents. This rule can be expressed as:

• $a^m \times a^n = a^{m+n}$

In this equation, both terms $4^5$ have the same base $4$.

According to the multiplication of powers rule:

• $4^5 \times 4^5 = 4^{5+5}$

Now, simply add the exponents:

$4^{5+5} = 4^{10}$

The simplified form of $4^5 \times 4^5$ is therefore $4^{10}$.

To simplify the expression $5^8 \times 5^3$, we will use the exponent rule which states that when multiplying powers with the same base, we add the exponents:

Step-by-step:

• Identify the base and exponents: Here, the base is $5$, and the exponents are $8$ and $3$.

• Apply the multiplication of exponents rule: $5^8 \times 5^3 = 5^{8+3}$.

Therefore, the correct answer is $5^{8+3}$.