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What is an equivalent expression for 7³ * 2³?

A. 7⁶ * 2⁶
B. 7⁹ * 2⁹
C. 7³ * 2⁶
D. 7⁶ * 2³

User Ryenus
by
8.2k points

1 Answer

4 votes

Final answer:

The expression 7³ * 2³ evaluates to 14³ which is equivalent to the numerical value of 2744. The given options do not represent the correct process or outcome.

Step-by-step explanation:

To find an equivalent expression for 7³ * 2³, we need to apply the properties of exponents. Since both terms have the same exponent, we can multiply the bases first and then apply the exponent.

Therefore, we first calculate 7 * 2, which equals 14, and then raise it to the third power to get the equivalent expression. 14³, which is the same as 7³ * 2³ because of the commutative property of multiplication and the power of a product property.

Now, it's clear that the expression 14³ does not match any of the options provided. So, we need to find a different way to express 7³ * 2³. What we're actually doing is calculating the result of and separately and then multiplying them. Since the exponents are the same, we do not multiply the exponents; we multiply the results of each base raised to that power. Thus, 7³ gives us 343, and 2³ gives us 8.

Then the product of 343 and 8 gives the final result, which is 2744. None of the answer choices (A. 7⁶ * 2⁶ B. 7⁹ * 2⁹ C. 7³ * 2⁶ D. 7⁶ * 2³) represent this process properly, so either there is a mistake in the options, or there might be additional context that could lead to one of these options being correct.

User Samuel Robert
by
7.4k points
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