Question

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

Answer 1

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?

Answer 2

it still doesnt make since

Answer 3

Do you know what an exponent is?

Answer 4

yes

Answer 5

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?

Answer 6

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.

Answer 7

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

Answer 8

its true

Answer 9

i think its choice D

Answer 10

Correct B is true, so that's not it.

Now we need to deal with C and D.

Answer 11

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.

Answer 12

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

Answer 13

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.

Answer 14

ok thanks so much for explaining things to me

Answer 15

You're welcome.