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Which expression is equivalent to $4^7 \times 4^4$ ? $\newline$ Choices: $\newline$ (A) $4^{11}$ $\newline$ (B) $\frac{1}{4^{11}}$ $\newline$ (C) $4^{28}$ $\newline$ (D) $\frac{1}{4^{28}}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

4^7 \times 4^4

?

\newline

Choices:

\newline

(A)

4^{11}

\newline

(B)

\frac{1}{4^{11}}

\newline

(C)

4^{28}

\newline

(D)

\frac{1}{4^{28}}

Identify Base and Exponents: Identify the base and the exponents in the expression $4^7 \times 4^4$ . $\newline$ Base: $4$ $\newline$ Exponents: $7, 4$
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. $\newline$ $4^7 \times 4^4 = 4^{7+4}$
Perform Exponent Addition: Perform the addition of the exponents. $\newline$ $7 + 4 = 11$ $\newline$ So, $4^7 \times 4^4 = 4^{11}$
Choose Equivalent Expression: Choose the equivalent expression for $4^7 \times 4^4$ . The correct expression is $4^{11}$ .

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