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Which expression is equivalent to $7^3 \times 7^3$ ? $\newline$ Choices: $\newline$ (A) $7^9$ $\newline$ (B) $\frac{1}{7^6}$ $\newline$ (C) $7^6$ $\newline$ (D) $\frac{1}{7^9}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

7^3 \times 7^3

?

\newline

Choices:

\newline

(A)

7^9

\newline

(B)

\frac{1}{7^6}

\newline

(C)

7^6

\newline

(D)

\frac{1}{7^9}

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In the expression $7^3 \times 7^3$ , $7$ is the base and both exponents are $3$ . $\newline$ Base: $7$ $\newline$ Exponents: $3, 3$
Apply Multiplication Rule: Apply the rule for multiplying powers with the same base. $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $7^3 \times 7^3 = 7^{(3+3)}$
Perform Exponent Addition: Perform the addition of the exponents. $7^{3+3} = 7^6$
Choose Equivalent Expression: Choose the equivalent expression for $7^3 \times 7^3$ . $\newline$ From the given choices, $7^6$ is the correct equivalent expression.

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