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

Question

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Answer 1

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 2

Find the numerical equivalent of 3^9 x 3^-5
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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 \( 81 \).