QuestionSimplify $4^{0} \cdot 4^{2}$ using exponent rules and show only positive exponents.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $4^{0} \cdot4^{}$ . . We need to simplify this expression using the properties of exponents.
3. We need to expand any numerical portion of our answer.
4. We should only include positive exponents in our final answer.

STEP 2

First, we need to understand the properties of exponents. One of the properties states that when we multiply two expressions with the same base, we can add the exponents. $a^{m} \cdot a^{n} = a^{m+n}$

STEP 3

Another property of exponents states that any number raised to the power of0 is1.
$a^{0} =1$

STEP 4

Now, we can apply these properties to our given expression. First, let's simplify $4^{0}$ .
$4^{0} =1$

STEP 5

So, our expression becomes $1 \cdot4^{2}$

STEP 6

Now, we can simplify $4^{2}$ .
$4^{2} =16$

STEP 7

So, our expression becomes $1 \cdot16$

STEP 8

Finally, we can simplify the expression by multiplying1 by16.
$1 \cdot16 =16$ The simplified expression is16.

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QuestionSimplify $4^{0} \cdot 4^{2}$ using exponent rules and show only positive exponents.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $4^{0} \cdot4^{}$ . . We need to simplify this expression using the properties of exponents.
3. We need to expand any numerical portion of our answer.
4. We should only include positive exponents in our final answer.

STEP 2

First, we need to understand the properties of exponents. One of the properties states that when we multiply two expressions with the same base, we can add the exponents. $a^{m} \cdot a^{n} = a^{m+n}$

STEP 3

Another property of exponents states that any number raised to the power of0 is1.
$a^{0} =1$

STEP 4

Now, we can apply these properties to our given expression. First, let's simplify $4^{0}$ .
$4^{0} =1$

STEP 5

So, our expression becomes $1 \cdot4^{2}$

STEP 6

Now, we can simplify $4^{2}$ .
$4^{2} =16$

STEP 7

So, our expression becomes $1 \cdot16$

STEP 8

Finally, we can simplify the expression by multiplying1 by16.
$1 \cdot16 =16$ The simplified expression is16.

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QuestionSimplify 40⋅424^{0} \cdot 4^{2}40⋅42 using exponent rules and show only positive exponents.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 40⋅44^{0} \cdot4^{}40⋅4. . We need to simplify this expression using the properties of exponents.3. We need to expand any numerical portion of our answer.4. We should only include positive exponents in our final answer.

STEP 2

First, we need to understand the properties of exponents. One of the properties states that when we multiply two expressions with the same base, we can add the exponents.am⋅an=am+na^{m} \cdot a^{n} = a^{m+n}am⋅an=am+n

STEP 3

Another property of exponents states that any number raised to the power of0 is1.a0=1a^{0} =1a0=1

STEP 4

Now, we can apply these properties to our given expression. First, let's simplify 404^{0}40.40=14^{0} =140=1

STEP 5

So, our expression becomes1⋅421 \cdot4^{2}1⋅42

STEP 6

Now, we can simplify 424^{2}42.42=164^{2} =1642=16

STEP 7

So, our expression becomes1⋅161 \cdot161⋅16

STEP 8

Finally, we can simplify the expression by multiplying1 by16.1⋅16=161 \cdot16 =161⋅16=16The simplified expression is16.

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QuestionSimplify $4^{0} \cdot 4^{2}$ using exponent rules and show only positive exponents.

Assumptions1. We are given the expression $4^{0} \cdot4^{}$ . . We need to simplify this expression using the properties of exponents.
3. We need to expand any numerical portion of our answer.
4. We should only include positive exponents in our final answer.

First, we need to understand the properties of exponents. One of the properties states that when we multiply two expressions with the same base, we can add the exponents. $a^{m} \cdot a^{n} = a^{m+n}$

Another property of exponents states that any number raised to the power of0 is1.
$a^{0} =1$

Now, we can apply these properties to our given expression. First, let's simplify $4^{0}$ .
$4^{0} =1$

So, our expression becomes $1 \cdot4^{2}$

Now, we can simplify $4^{2}$ .
$4^{2} =16$

So, our expression becomes $1 \cdot16$

Finally, we can simplify the expression by multiplying1 by16.
$1 \cdot16 =16$ The simplified expression is16.