Select all the expressions that are equivalent to $4 \times 4^7$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{4^{-8}}$ $\newline$ (B) $4^8$ $\newline$ (C) $\frac{1}{4^8}$ $\newline$ (D) $4^7$

Full solution

Q. Select all the expressions that are equivalent to

4 \times 4^7

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{4^{-8}}

\newline

(B)

4^8

\newline

(C)

\frac{1}{4^8}

\newline

(D)

4^7

Understand Given Expression: Understand the given expression and the properties of exponents. $\newline$ The given expression is $4 \times 4^7$ . According to the properties of exponents, when we multiply two powers with the same base, we add the exponents.
Apply Exponent Rule: Apply the exponent rule to the given expression. $4 \times 4^7$ can be written as $4^1 \times 4^7$ , which simplifies to $4^{(1+7)} = 4^8$ .
Compare with Choices: Compare the simplified expression with the choices. $\newline$ We have found that $4 \times 4^7$ simplifies to $4^8$ . Now we need to check which of the given choices are equivalent to $4^8$ . $\newline$ (A) $\frac{1}{4^{-8}}$ : This is equivalent to $4^8$ because a negative exponent means the reciprocal of the base raised to the positive exponent. $\newline$ (B) $4^8$ : This is clearly equivalent to $4^8$ . $\newline$ (C) $\frac{1}{4^8}$ : This is the reciprocal of $4^8$ , so it is not equivalent. $\newline$ (D) $4^7$ : This is not equivalent because it is missing the multiplication by $4^8$ $0$ .