Math  /  Algebra

QuestionFollow the instructions below.
Write b3b2b^{3} \cdot b^{2} without exponents. b3b2=b^{3} \cdot b^{2}= \square
Fill in the blank. b3b2=b[b^{3} \cdot b^{2}=b^{[ }

Studdy Solution

STEP 1

What is this asking? We're asked to simplify the multiplication of two exponential terms with the same base, bb, and then write the simplified expression both without exponents and as a single term with an exponent. Watch out! Don't accidentally multiply the exponents together.
Remember, when multiplying exponential terms with the same base, we *add* the exponents.

STEP 2

1. Expand the terms.
2. Multiply the expanded terms.
3. Rewrite using exponents.

STEP 3

Let's break down what b3b^3 and b2b^2 actually mean! b3b^3 means bb multiplied by itself **3** times: bbbb \cdot b \cdot b.

STEP 4

Similarly, b2b^2 means bb multiplied by itself **2** times: bbb \cdot b.

STEP 5

Now, let's multiply these expanded terms together!
We have b3b2=(bbb)(bb)b^3 \cdot b^2 = (b \cdot b \cdot b) \cdot (b \cdot b).

STEP 6

This gives us bb multiplied by itself a total of **5** times: bbbbbb \cdot b \cdot b \cdot b \cdot b.
This is the simplified expression *without* exponents.

STEP 7

Since we're multiplying bb by itself **5** times, we can rewrite this using an exponent as b5b^5.
Remember, the exponent tells us how many times the base is multiplied by itself.

STEP 8

b3b2=bbbbbb^{3} \cdot b^{2} = b \cdot b \cdot b \cdot b \cdot b b3b2=b5b^{3} \cdot b^{2} = b^{5}

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