Multiplication of Powers Practice Problems & Solutions

To solve the expression $7^9 \times 7^1$, we need to apply the rules of exponents, specifically the multiplication of powers rule. According to this rule, when we multiply two powers with the same base, we keep the base and add the exponents together.

• The expression can be written as $a^m \times a^n = a^{m+n}$, where $a$ is the base and $m$ and $n$ are the exponents.
• In this case, our base $a$ is 7, and our exponents are 9 and 1.
• Applying the formula, we have: $7^9 \times 7^1 = 7^{9+1}$.
• Simplifying the exponent: $9 + 1 = 10$.

Thus, the expression simplifies to: $7^{10}$.

To solve the exercise we use the property of multiplication of powers with the same bases:

$a^n * a^m = a^{n+m}$

With the help of this property, we can add the exponents.

$4^2\times4^4=4^{4+2}=4^6$

To solve the problem of simplifying the equation $11^{10} \times 11^{11}$, follow these steps:

• Step 1: Identify that the bases are the same (11).

• Step 2: Apply the multiplication of powers rule, which states that when multiplying like bases, you add the exponents.

• Step 3: Add the exponents: $10 + 11$.

• Step 4: Perform the addition: $10 + 11 = 21$.

• Step 5: Write the expression with the new exponent: $11^{10+11}= 11^{21}$.

Therefore, the simplified expression is $11^{21}$. This corresponds to options 1 and 2 being correct as they represent the same expression when evaluating the sum, which is also represented by choice 4 as "a'+b' are correct".

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 solve the problem of simplifying $5 \times 5^8$, we use the rules of exponents:

• Identify that $5$ can be rewritten as $5^1$.
• Apply the multiplication of powers rule: $a^m \times a^n = a^{m+n}$.
• Add the exponents: $1 + 8 = 9$.
• Thus, $5^1 \times 5^8 = 5^{1+8} = 5^9$.

Therefore, the simplified form of the given expression is $5^9$.

Hence, the correct answer is choice : $5^9$.