Question

Find the numerical equivalent of 7^2 x 7^3
_____

Answer 1

Find the numerical equivalent of 3^9 x 3^-5
_____

Answer 2

To find the numerical equivalent of \( 7^2 \times 7^3 \), you can use the properties of exponents. When multiplying two expressions with the same base, you can add their exponents:

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

Now, calculate \( 7^5 \):

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

Calculating step-by-step:

\[
7 \times 7 = 49
\]
\[
49 \times 7 = 343
\]
\[
343 \times 7 = 2401
\]
\[
2401 \times 7 = 16807
\]

Therefore,

\[
7^2 \times 7^3 = 7^5 = 16807
\]

The numerical equivalent is \( 16807 \).

Answer 3

To find the numerical equivalent of \( 3^9 \times 3^{-5} \), you can use the properties of exponents. Specifically, when multiplying two expressions with the same base, you can add their exponents:

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

Now, calculate \( 3^4 \):

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

Calculating step-by-step:

\[
3 \times 3 = 9
\]
\[
9 \times 3 = 27
\]
\[
27 \times 3 = 81
\]

Therefore,

\[
3^9 \times 3^{-5} = 3^4 = 81
\]

The numerical equivalent is \( 81 \).