1. 2p x 3q - 4r = 2. 4u x 3u x v x u x 2v = 3. (-2k4)3 = 4. 2f2 x 3g x (-3f) =

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(1) `2p * 3q - 4r`

To simplify, multiply the numbers and copy the letters.

`=6pq - 4r`

Since the two are unlike terms, they cannot be subtracted.

Therefore, the simplified form of the given expression is `2p*3q - 4r = 6pq - 4r.`

(2) `4u * 3u * v...

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(1) `2p * 3q - 4r`

To simplify, multiply the numbers and copy the letters.

`=6pq - 4r`

Since the two are unlike terms, they cannot be subtracted.

Therefore, the simplified form of the given expression is `2p*3q - 4r = 6pq - 4r.`

(2) `4u * 3u * v * u * 2v`

Multiplying the numbers, the expression becomes:

`= 24u * u * v*u*v.`

To multiply same letters, apply the exponent rule `a^m*a^n=a^(m+n).`

`=24u^(1+1+1)* v^(1+1)`

`=24u^3v^2`

Thus, the simplified form is `4u*3u*v*u*2v=24u^3v^2.`

(3) `(-2k^4)^3`

To simplify, apply the exponent rule `(ab)^m=a^mb^m.`

`=(-2)^3(k^4)^3`

When the exponent of a negative number is odd, the result is a negative number.

`=-8(k^4)^3`

And then, apply the exponent rule `(a^m)^n=a^(m*n).`

`=-8k^12`

Therefore, the simplified form is `(-2k^4)^3=-8k^12.`

(4) `2f^2*3g*(-3f)`

Multiplying the numbers, this expression becomes:

`=-18f^2*g*f.`

To multiply same letters, apply the exponent rule `a^m*a^n=a^(m+n).`

`=-18f^(2+1)*g`

`=-18f^3g`

Hence, the simplified form of the given expression is `2f^2*3g*(-3f)=-18f^3g.`

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