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countrygirl1431

  • one year ago

Which of the following statements is not true? xxxxxx = x6 AAAAAAABBBBB = A7B5 b6c6 = (bc)6 x5y5z5 = xyz5

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  1. mathstudent55
    • one year ago
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    An integer exponent greater than 1 is the number of the same factors being multiplied together. For example, \(y^2 = y \times y = yy\) With that in mind, do you think that A and B are true or false?

  2. countrygirl1431
    • one year ago
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    it still doesnt make since

  3. mathstudent55
    • one year ago
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    Do you know what an exponent is?

  4. countrygirl1431
    • one year ago
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    yes

  5. mathstudent55
    • one year ago
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    An exponent is a way of writing a multiplication of the same number. For example, if you want to write \(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\) you can use an exponent to write simply \(4^7\) \(4^7\) is much quicker to write than \(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\) and takes much less space. Since there are 7 factors of 4 being multiplied together, you write 4 as a base, and you write the exponent 7. The same way, \(x^3 = x \times x \times x\) \(x^3\) is simply a short way of writing the multiplication \(x \times x \times x\) Ok so far?

  6. mathstudent55
    • one year ago
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    Now look at choice A. \(xxxxxx = x^6\) When variables are next to each other with no operation in between, that means multiplication. On the let side you have 6 x's being multiplied together. Since the factors are all the same, x, we can use an exponent to write that in a shorter way. Since there are 6 x's, that means we write a base of x and an exponent of 6. That means \(xxxxxx = x^6\) is correct. This means choice A is true, so it is not the answer to this problem. Remember, we are looking for the choice that is a false statement.

  7. mathstudent55
    • one year ago
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    Now look at choice B. According to the meaning of exponents you saw above, is choice B true or false?

  8. countrygirl1431
    • one year ago
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    its true

  9. countrygirl1431
    • one year ago
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    i think its choice D

  10. mathstudent55
    • one year ago
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    Correct B is true, so that's not it. Now we need to deal with C and D.

  11. mathstudent55
    • one year ago
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    Here is a rule of exponents: \((ab)^n = a^nb^n\) When you raise a product to an exponent, you need to raise every factor to the exponent. Look at C. \(b^6c^6 = (bc)^6\) On the right side, you are raising a product to the 6th power. To raise the product bc to the 6th power, you need to raise each factor to the 6th power. That means \((bc)^6 = b^6c^6\) This is exactly what we have in choice C only in reverse order. Choice C is true.

  12. mathstudent55
    • one year ago
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    You are correct. By the process of elimination, D must be the false statement, but we should see why.

  13. mathstudent55
    • one year ago
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    Choice D. \(x^5y^5z^5 = xyz^5\) Look at the left side. Every factor x, y, and z, is raised to the 5th power. Using our rule above in reverse, that means \(x^5y^5z^5 = (xyz)^5\) The statement of choice D has only \(xyz^5\) on the right side. \(x^5y^5z^5 \ne xyz^5\) This means this statement is false and is the answer to the question.

  14. countrygirl1431
    • one year ago
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    ok thanks so much for explaining things to me

  15. mathstudent55
    • one year ago
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    You're welcome.

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