Math / Algebra

QuestionSimplify each expression. 1) $4 u^{9} \times\left(-2 u^{3}\right)=$

Studdy Solution

STEP 1

1. The expression $4 u^9 \times (-2 u^3)$ involves multiplication of monomials.
2. The properties of exponents and multiplication apply.

STEP 2

1. Multiply the coefficients of the monomials.
2. Add the exponents of the like bases.

STEP 3

Identify the coefficients and the bases with their exponents.
The coefficients are $4$ and $-2$ . The base is $u$ with exponents $9$ and $3$ .

STEP 4

Multiply the coefficients of the monomials.
$4 \times (-2) = -8$

STEP 5

Add the exponents of the like bases.
$u^9 \times u^3 = u^{9+3} = u^{12}$

STEP 6

Combine the results from the multiplication of coefficients and the addition of exponents.
$4 u^9 \times (-2 u^3) = -8 u^{12}$
Solution: $4 u^9 \times (-2 u^3) = -8 u^{12}$

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QuestionSimplify each expression. 1) $4 u^{9} \times\left(-2 u^{3}\right)=$

Studdy Solution

STEP 1

1. The expression $4 u^9 \times (-2 u^3)$ involves multiplication of monomials.
2. The properties of exponents and multiplication apply.

STEP 2

1. Multiply the coefficients of the monomials.
2. Add the exponents of the like bases.

STEP 3

Identify the coefficients and the bases with their exponents.
The coefficients are $4$ and $-2$ . The base is $u$ with exponents $9$ and $3$ .

STEP 4

Multiply the coefficients of the monomials.
$4 \times (-2) = -8$

STEP 5

Add the exponents of the like bases.
$u^9 \times u^3 = u^{9+3} = u^{12}$

STEP 6

Combine the results from the multiplication of coefficients and the addition of exponents.
$4 u^9 \times (-2 u^3) = -8 u^{12}$
Solution: $4 u^9 \times (-2 u^3) = -8 u^{12}$

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QuestionSimplify each expression. 1) 4u9×(−2u3)=4 u^{9} \times\left(-2 u^{3}\right)=4u9×(−2u3)=

Studdy Solution

STEP 1

1. The expression 4u9×(−2u3)4 u^9 \times (-2 u^3)4u9×(−2u3) involves multiplication of monomials.2. The properties of exponents and multiplication apply.

STEP 2

1. Multiply the coefficients of the monomials.2. Add the exponents of the like bases.

STEP 3

Identify the coefficients and the bases with their exponents.The coefficients are 444 and −2-2−2. The base is uuu with exponents 999 and 333.

STEP 4

Multiply the coefficients of the monomials.4×(−2)=−8 4 \times (-2) = -8 4×(−2)=−8

STEP 5

Add the exponents of the like bases.u9×u3=u9+3=u12 u^9 \times u^3 = u^{9+3} = u^{12} u9×u3=u9+3=u12

STEP 6

Combine the results from the multiplication of coefficients and the addition of exponents.4u9×(−2u3)=−8u12 4 u^9 \times (-2 u^3) = -8 u^{12} 4u9×(−2u3)=−8u12Solution: 4u9×(−2u3)=−8u12 4 u^9 \times (-2 u^3) = -8 u^{12} 4u9×(−2u3)=−8u12

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QuestionSimplify each expression. 1) $4 u^{9} \times\left(-2 u^{3}\right)=$

1. The expression $4 u^9 \times (-2 u^3)$ involves multiplication of monomials.
2. The properties of exponents and multiplication apply.

1. Multiply the coefficients of the monomials.
2. Add the exponents of the like bases.

Identify the coefficients and the bases with their exponents.
The coefficients are $4$ and $-2$ . The base is $u$ with exponents $9$ and $3$ .

Multiply the coefficients of the monomials.
$4 \times (-2) = -8$

Add the exponents of the like bases.
$u^9 \times u^3 = u^{9+3} = u^{12}$

Combine the results from the multiplication of coefficients and the addition of exponents.
$4 u^9 \times (-2 u^3) = -8 u^{12}$
Solution: $4 u^9 \times (-2 u^3) = -8 u^{12}$