Math / Algebra

Question10 Multiple Choice 1 point Simplify the exponential expression. $(-4x^4y^7)^2$ $-16x^8y^{14}$ $16x^8y^{14}$ $16x^6y^9$ $-4x^8y^{14}$ Clear my selection

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression $(-4x^4y^7)^2$ . Watch out! Don't forget to square everything inside the parentheses, including the $-4$ !
And remember your exponent rules!

STEP 2

1. Distribute the exponent.
2. Simplify the terms.

STEP 3

Alright, let's distribute that exponent of $2$ to each term inside the parentheses.
Remember, this means we're multiplying the exponents of each term by $2$ .
Why? Because raising a power to a power means we multiply the exponents!
It's like saying we have two sets of parentheses multiplied together, each containing $-4x^4y^7$ .

STEP 4

So, we have $(-4)^2 \cdot (x^4)^2 \cdot (y^7)^2$ .
See how we applied the exponent to each piece?
This is super important!

STEP 5

Let's simplify each part.
First, $(-4)^2$ means $-4$ times $-4$ , which gives us a positive 16.
Remember, a negative times a negative is a positive!

STEP 6

Next, $(x^4)^2$ .
When we raise a power to a power, we multiply the exponents.
So, $4 \cdot 2 = 8$ , giving us $x^8$ .

STEP 7

Finally, $(y^7)^2$ .
Again, multiply those exponents: $7 \cdot 2 = 14$ , resulting in $y^{14}$ .

STEP 8

Putting it all together, we have $16x^8y^{14}$ .
Boom!

STEP 9

Our simplified expression is $16x^8y^{14}$ .

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Question10 Multiple Choice 1 point Simplify the exponential expression. $(-4x^4y^7)^2$ $-16x^8y^{14}$ $16x^8y^{14}$ $16x^6y^9$ $-4x^8y^{14}$ Clear my selection

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression $(-4x^4y^7)^2$ . Watch out! Don't forget to square everything inside the parentheses, including the $-4$ !
And remember your exponent rules!

STEP 2

1. Distribute the exponent.
2. Simplify the terms.

STEP 3

STEP 4

So, we have $(-4)^2 \cdot (x^4)^2 \cdot (y^7)^2$ .
See how we applied the exponent to each piece?
This is super important!

STEP 5

Let's simplify each part.
First, $(-4)^2$ means $-4$ times $-4$ , which gives us a positive 16.
Remember, a negative times a negative is a positive!

STEP 6

Next, $(x^4)^2$ .
When we raise a power to a power, we multiply the exponents.
So, $4 \cdot 2 = 8$ , giving us $x^8$ .

STEP 7

Finally, $(y^7)^2$ .
Again, multiply those exponents: $7 \cdot 2 = 14$ , resulting in $y^{14}$ .

STEP 8

Putting it all together, we have $16x^8y^{14}$ .
Boom!

STEP 9

Our simplified expression is $16x^8y^{14}$ .

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Question10 Multiple Choice 1 point Simplify the exponential expression. (−4x4y7)2(-4x^4y^7)^2(−4x4y7)2 −16x8y14-16x^8y^{14}−16x8y14 16x8y1416x^8y^{14}16x8y14 16x6y916x^6y^916x6y9 −4x8y14-4x^8y^{14}−4x8y14 Clear my selection

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression (−4x4y7)2(-4x^4y^7)^2(−4x4y7)2. Watch out! Don't forget to square *everything* inside the parentheses, including the −4-4−4!And remember your exponent rules!

STEP 2

1. Distribute the exponent.2. Simplify the terms.

STEP 3

STEP 4

So, we have (−4)2⋅(x4)2⋅(y7)2(-4)^2 \cdot (x^4)^2 \cdot (y^7)^2(−4)2⋅(x4)2⋅(y7)2.See how we applied the exponent to each piece?This is super important!

STEP 5

Let's simplify each part.First, (−4)2(-4)^2(−4)2 means −4-4−4 times −4-4−4, which gives us a positive **16**.Remember, a negative times a negative is a positive!

STEP 6

Next, (x4)2(x^4)^2(x4)2.When we raise a power to a power, we multiply the exponents.So, 4⋅2=84 \cdot 2 = 84⋅2=8, giving us x8x^8x8.

STEP 7

Finally, (y7)2(y^7)^2(y7)2.Again, multiply those exponents: 7⋅2=147 \cdot 2 = 147⋅2=14, resulting in y14y^{14}y14.

STEP 8

Putting it all together, we have 16x8y1416x^8y^{14}16x8y14.Boom!

STEP 9

Our simplified expression is 16x8y1416x^8y^{14}16x8y14.

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Question10 Multiple Choice 1 point Simplify the exponential expression. $(-4x^4y^7)^2$ $-16x^8y^{14}$ $16x^8y^{14}$ $16x^6y^9$ $-4x^8y^{14}$ Clear my selection

What is this asking? We need to simplify the expression $(-4x^4y^7)^2$ . Watch out! Don't forget to square everything inside the parentheses, including the $-4$ !
And remember your exponent rules!

1. Distribute the exponent.
2. Simplify the terms.

So, we have $(-4)^2 \cdot (x^4)^2 \cdot (y^7)^2$ .
See how we applied the exponent to each piece?
This is super important!

Let's simplify each part.
First, $(-4)^2$ means $-4$ times $-4$ , which gives us a positive 16.
Remember, a negative times a negative is a positive!

Next, $(x^4)^2$ .
When we raise a power to a power, we multiply the exponents.
So, $4 \cdot 2 = 8$ , giving us $x^8$ .

Finally, $(y^7)^2$ .
Again, multiply those exponents: $7 \cdot 2 = 14$ , resulting in $y^{14}$ .

Putting it all together, we have $16x^8y^{14}$ .
Boom!

Our simplified expression is $16x^8y^{14}$ .