Question

Use the Product Rule of Exponents to simplify the expression 2^4 times 2^2.

Answer 1

To simplify the expression \( 2^4 \times 2^2 \) using the Product Rule of Exponents, you add the exponents when multiplying like bases. The rule states:

\[
a^m \times a^n = a^{m+n}
\]

Applying this to the given expression:

\[
2^4 \times 2^2 = 2^{4+2}
\]

Now, calculate the sum of the exponents:

\[
4 + 2 = 6
\]

Thus, the expression simplifies to:

\[
2^6
\]

So, \( 2^4 \times 2^2 = 2^6 \).

Answer 2

Use the Product Rule of Exponents to simplify the expression 3^8 times 3^3.

Answer 3

To simplify the expression \( 3^8 \times 3^3 \) using the Product Rule of Exponents, you add the exponents when multiplying like bases. The Product Rule states:

\[
a^m \times a^n = a^{m+n}
\]

Applying this to the given expression:

\[
3^8 \times 3^3 = 3^{8+3}
\]

Now, calculate the sum of the exponents:

\[
8 + 3 = 11
\]

Thus, the expression simplifies to:

\[
3^{11}
\]

So, \( 3^8 \times 3^3 = 3^{11} \).

Answer 4

Find the numerical equivalent of 7^2 times 7^3.

Answer 5

To find the numerical equivalent of \( 7^2 \times 7^3 \), we can first apply the Product Rule of Exponents, which states:

\[
a^m \times a^n = a^{m+n}
\]

So we have:

\[
7^2 \times 7^3 = 7^{2+3} = 7^5
\]

Next, we calculate \( 7^5 \):

\[
7^5 = 7 \times 7 \times 7 \times 7 \times 7
\]

Calculating step by step:

1. \( 7 \times 7 = 49 \)
2. \( 49 \times 7 = 343 \)
3. \( 343 \times 7 = 2401 \)
4. \( 2401 \times 7 = 16807 \)

Thus, the numerical equivalent of \( 7^2 \times 7^3 \) is:

\[
7^5 = 16807
\]

Answer 6

Find the numerical equivalent of 3^9 times 3^-5

Answer 7

To find the numerical equivalent of \( 3^9 \times 3^{-5} \), we can use the Product Rule of Exponents, which states:

\[
a^m \times a^n = a^{m+n}
\]

Applying this rule, we have:

\[
3^9 \times 3^{-5} = 3^{9 + (-5)} = 3^{9 - 5} = 3^{4}
\]

Now, let's calculate \( 3^4 \):

\[
3^4 = 3 \times 3 \times 3 \times 3
\]

Calculating this step by step:

1. \( 3 \times 3 = 9 \)
2. \( 9 \times 3 = 27 \)
3. \( 27 \times 3 = 81 \)

Thus, the numerical equivalent of \( 3^9 \times 3^{-5} \) is:

\[
3^4 = 81
\]