Select all the expressions that are equivalent to 4 * 4^7. Multi-select Choices: (A)1/4^-8 (B)4^8 (C)1/4^8 (D)4^7

Understand Given Expression: Understand the given expression and the properties of exponents. The given expression is 4 * 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 * 4^7 can be written as 4^1 * 4^7, which simplifies to 4^(1+7) = 4^8.Compare with Choices: Compare the simplified expression with the choices. We have found that 4 * 4^7 simplifies to 4^8. Now we need to check which of the given choices are equivalent to 4^8. (A) 1/4^-8: This is equivalent to 4^8 because a negative exponent means the reciprocal of the base raised to the positive exponent. (B) 4^8: This is clearly equivalent to 4^8. (C) 1/4^8: This is the reciprocal of 4^8, so it is not equivalent. (D) 4^7: This is not equivalent because it is missing the multiplication by 4.

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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) $4^7$

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

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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 $4^8$ $0$ .