Question

The expression cube root of, 7, squared, end cube root, dot, cube root of, 7, to the power 4 , end cube root

3

7
2

​
⋅
3

7
4

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is equivalent to
Answer
Multiple Choice Answers
7, start superscript, one half, end superscript7
2
1
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7, start superscript, start fraction, 8, divided by, 9, end fraction, end superscript7
9
8
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7, start superscript, start fraction, 9, divided by, 8, end fraction, end superscript7
8
9
​


7, squared7
2

Answer 1

To solve the expression involving cube roots and powers of 7, we convert the cube roots into fractional exponents and add the exponents together, resulting in 7 squared.

Step-by-step explanation:

The expression given is the cube root of 7 squared multiplied by the cube root of 7 to the power of 4. To solve this, we can apply the rule for multiplying powers with the same base, which tells us to add the exponents. In this case, the cube root can be expressed as a fractional exponent of 1/3.

The expression cube root of 7 squared, end cube root, dot, cube root of 7 to the power 4, end cube root 3 is equivalent to 71/272. To simplify this expression, we can apply the property of exponents which states that when you raise a power to another power, you multiply the exponents. So the expression becomes 7(1/2 + 2) which is equal to 7(5/2).

Therefore, 7 squared is 7 to the power of 2/3, and 7 to the power of 4 is 7 to the power of 4/3. Multiplying these together, we get 7 to the power of 2/3 times 7 to the power of 4/3, which simplifies to 7 to the power of (2/3 + 4/3), or 7 to the power of 6/3, which is just 7 squared.