## countrygirl1431 one year ago Which of the following statements is not true? xxxxxx = x6 AAAAAAABBBBB = A7B5 b6c6 = (bc)6 x5y5z5 = xyz5

1. mathstudent55

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

it still doesnt make since

3. mathstudent55

Do you know what an exponent is?

4. countrygirl1431

yes

5. mathstudent55

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

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

Now look at choice B. According to the meaning of exponents you saw above, is choice B true or false?

8. countrygirl1431

its true

9. countrygirl1431

i think its choice D

10. mathstudent55

Correct B is true, so that's not it. Now we need to deal with C and D.

11. mathstudent55

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

You are correct. By the process of elimination, D must be the false statement, but we should see why.

13. mathstudent55

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

ok thanks so much for explaining things to me

15. mathstudent55

You're welcome.