Math / Algebra

QuestionRewrite the expression $4^{-2} \cdot 8^{0} \cdot 5^{6}$ using only positive exponents. $\frac{5^{6}}{4^{2} \cdot 8}$ $\frac{4^{2}}{5^{6}}$ $\frac{8 \cdot 5^{6}}{4^{2}}$ $\frac{5^{6}}{4^{2}}$

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression with exponents and make sure all the exponents are positive! Watch out! Don't forget the rules of exponents!
A negative exponent means "reciprocal," not "negative number." Also, anything (except 0) raised to the power of 0 is 1!

STEP 2

1. Handle the negative exponent
2. Handle the zero exponent
3. Combine and simplify

STEP 3

Alright, let's rewrite that $4^{-2}$ .
Remember, a negative exponent means "take the reciprocal," so $4^{-2}$ becomes $\frac{1}{4^{2}}$ .
It's like flipping it!
So our expression is now $\frac{1}{4^{2}} \cdot 8^{0} \cdot 5^{6}$ .

STEP 4

Now, let's look at $8^0$ .
Anything (except 0) raised to the power of zero is 1!
So, $8^0 = 1$ .
Our expression becomes $\frac{1}{4^{2}} \cdot 1 \cdot 5^{6}$ .
Multiplying by 1 doesn't change anything, so we can simplify to $\frac{1}{4^{2}} \cdot 5^{6}$ .

STEP 5

Let's put it all together!
We have $\frac{1}{4^{2}} \cdot 5^{6}$ , which is the same as $\frac{5^{6}}{4^{2}}$ .
That's it!
All exponents are positive, and we've simplified the expression.

STEP 6

Our final simplified expression is $\frac{5^{6}}{4^{2}}$ .

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QuestionRewrite the expression $4^{-2} \cdot 8^{0} \cdot 5^{6}$ using only positive exponents. $\frac{5^{6}}{4^{2} \cdot 8}$ $\frac{4^{2}}{5^{6}}$ $\frac{8 \cdot 5^{6}}{4^{2}}$ $\frac{5^{6}}{4^{2}}$

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression with exponents and make sure all the exponents are positive! Watch out! Don't forget the rules of exponents!
A negative exponent means "reciprocal," not "negative number." Also, anything (except 0) raised to the power of 0 is 1!

STEP 2

1. Handle the negative exponent
2. Handle the zero exponent
3. Combine and simplify

STEP 3

Alright, let's rewrite that $4^{-2}$ .
Remember, a negative exponent means "take the reciprocal," so $4^{-2}$ becomes $\frac{1}{4^{2}}$ .
It's like flipping it!
So our expression is now $\frac{1}{4^{2}} \cdot 8^{0} \cdot 5^{6}$ .

STEP 4

Now, let's look at $8^0$ .
Anything (except 0) raised to the power of zero is 1!
So, $8^0 = 1$ .
Our expression becomes $\frac{1}{4^{2}} \cdot 1 \cdot 5^{6}$ .
Multiplying by 1 doesn't change anything, so we can simplify to $\frac{1}{4^{2}} \cdot 5^{6}$ .

STEP 5

Let's put it all together!
We have $\frac{1}{4^{2}} \cdot 5^{6}$ , which is the same as $\frac{5^{6}}{4^{2}}$ .
That's it!
All exponents are positive, and we've simplified the expression.

STEP 6

Our final simplified expression is $\frac{5^{6}}{4^{2}}$ .

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QuestionRewrite the expression 4−2⋅80⋅564^{-2} \cdot 8^{0} \cdot 5^{6}4−2⋅80⋅56 using only positive exponents. 5642⋅8\frac{5^{6}}{4^{2} \cdot 8}42⋅856​ 4256\frac{4^{2}}{5^{6}}5642​ 8⋅5642\frac{8 \cdot 5^{6}}{4^{2}}428⋅56​ 5642\frac{5^{6}}{4^{2}}4256​

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression with exponents and make sure all the exponents are positive! Watch out! Don't forget the rules of exponents!A negative exponent means "reciprocal," not "negative number." Also, anything (except 0) raised to the power of 0 is 1!

STEP 2

1. Handle the negative exponent2. Handle the zero exponent3. Combine and simplify

STEP 3

Alright, let's **rewrite** that 4−24^{-2}4−2.Remember, a negative exponent means "take the reciprocal," so 4−24^{-2}4−2 becomes 142\frac{1}{4^{2}}421​.It's like flipping it!So our expression is now 142⋅80⋅56\frac{1}{4^{2}} \cdot 8^{0} \cdot 5^{6}421​⋅80⋅56.

STEP 4

STEP 5

Let's put it all together!We have 142⋅56\frac{1}{4^{2}} \cdot 5^{6}421​⋅56, which is the same as 5642\frac{5^{6}}{4^{2}}4256​.That's it!All exponents are positive, and we've simplified the expression.

STEP 6

Our **final simplified expression** is 5642\frac{5^{6}}{4^{2}}4256​.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionRewrite the expression $4^{-2} \cdot 8^{0} \cdot 5^{6}$ using only positive exponents. $\frac{5^{6}}{4^{2} \cdot 8}$ $\frac{4^{2}}{5^{6}}$ $\frac{8 \cdot 5^{6}}{4^{2}}$ $\frac{5^{6}}{4^{2}}$

What is this asking? We're asked to simplify an expression with exponents and make sure all the exponents are positive! Watch out! Don't forget the rules of exponents!
A negative exponent means "reciprocal," not "negative number." Also, anything (except 0) raised to the power of 0 is 1!

1. Handle the negative exponent
2. Handle the zero exponent
3. Combine and simplify

Alright, let's rewrite that $4^{-2}$ .
Remember, a negative exponent means "take the reciprocal," so $4^{-2}$ becomes $\frac{1}{4^{2}}$ .
It's like flipping it!
So our expression is now $\frac{1}{4^{2}} \cdot 8^{0} \cdot 5^{6}$ .

Let's put it all together!
We have $\frac{1}{4^{2}} \cdot 5^{6}$ , which is the same as $\frac{5^{6}}{4^{2}}$ .
That's it!
All exponents are positive, and we've simplified the expression.

Our final simplified expression is $\frac{5^{6}}{4^{2}}$ .