Question Multiply and simplify the expression $6 x y^{3} z \cdot 3 x^{2} y x^{2}$ .

Studdy Solution

STEP 1

Assumptions
1. We are given two expressions to multiply: $6xy^{3}z$ and $3x^{2}yx^{2}$ .
2. We need to apply the laws of exponents and multiplication to simplify the expression.

STEP 2

First, we will multiply the coefficients (numerical parts) of the two expressions.
$6 \times 3$

STEP 3

Calculate the product of the coefficients.
$6 \times 3 = 18$

STEP 4

Next, we will multiply the variables with the same base by adding their exponents according to the laws of exponents.
For the variable $x$ , we have $x^1$ from the first expression and $x^{2+2}$ from the second expression.

STEP 5

Add the exponents of $x$ .
$1 + (2 + 2) = 5$

STEP 6

For the variable $y$ , we have $y^3$ from the first expression and $y^1$ from the second expression.

STEP 7

Add the exponents of $y$ .
$3 + 1 = 4$

STEP 8

For the variable $z$ , we only have $z^1$ from the first expression and no $z$ in the second expression.

STEP 9

Since there is only one $z$ , its exponent remains as $1$ .

STEP 10

Combine the results from steps 3, 5, 7, and 9 to write the simplified expression.
$18x^5y^4z$
The simplified result of multiplying and simplifying $6xy^{3}z \cdot 3x^{2}yx^{2}$ is $18x^5y^4z$ .

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Question Multiply and simplify the expression $6 x y^{3} z \cdot 3 x^{2} y x^{2}$ .

Studdy Solution

STEP 1

Assumptions
1. We are given two expressions to multiply: $6xy^{3}z$ and $3x^{2}yx^{2}$ .
2. We need to apply the laws of exponents and multiplication to simplify the expression.

STEP 2

First, we will multiply the coefficients (numerical parts) of the two expressions.
$6 \times 3$

STEP 3

Calculate the product of the coefficients.
$6 \times 3 = 18$

STEP 4

Next, we will multiply the variables with the same base by adding their exponents according to the laws of exponents.
For the variable $x$ , we have $x^1$ from the first expression and $x^{2+2}$ from the second expression.

STEP 5

Add the exponents of $x$ .
$1 + (2 + 2) = 5$

STEP 6

For the variable $y$ , we have $y^3$ from the first expression and $y^1$ from the second expression.

STEP 7

Add the exponents of $y$ .
$3 + 1 = 4$

STEP 8

For the variable $z$ , we only have $z^1$ from the first expression and no $z$ in the second expression.

STEP 9

Since there is only one $z$ , its exponent remains as $1$ .

STEP 10

Combine the results from steps 3, 5, 7, and 9 to write the simplified expression.
$18x^5y^4z$
The simplified result of multiplying and simplifying $6xy^{3}z \cdot 3x^{2}yx^{2}$ is $18x^5y^4z$ .

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Question Multiply and simplify the expression 6xy3z⋅3x2yx26 x y^{3} z \cdot 3 x^{2} y x^{2}6xy3z⋅3x2yx2.

Studdy Solution

STEP 1

Assumptions1. We are given two expressions to multiply: 6xy3z6xy^{3}z6xy3z and 3x2yx23x^{2}yx^{2}3x2yx2.2. We need to apply the laws of exponents and multiplication to simplify the expression.

STEP 2

First, we will multiply the coefficients (numerical parts) of the two expressions.6×36 \times 36×3

STEP 3

Calculate the product of the coefficients.6×3=186 \times 3 = 186×3=18

STEP 4

Next, we will multiply the variables with the same base by adding their exponents according to the laws of exponents.For the variable xxx, we have x1x^1x1 from the first expression and x2+2x^{2+2}x2+2 from the second expression.

STEP 5

Add the exponents of xxx.1+(2+2)=51 + (2 + 2) = 51+(2+2)=5

STEP 6

For the variable yyy, we have y3y^3y3 from the first expression and y1y^1y1 from the second expression.

STEP 7

Add the exponents of yyy.3+1=43 + 1 = 43+1=4

STEP 8

For the variable zzz, we only have z1z^1z1 from the first expression and no zzz in the second expression.

STEP 9

Since there is only one zzz, its exponent remains as 111.

STEP 10

Combine the results from steps 3, 5, 7, and 9 to write the simplified expression.18x5y4z18x^5y^4z18x5y4zThe simplified result of multiplying and simplifying 6xy3z⋅3x2yx26xy^{3}z \cdot 3x^{2}yx^{2}6xy3z⋅3x2yx2 is 18x5y4z18x^5y^4z18x5y4z.

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Question Multiply and simplify the expression $6 x y^{3} z \cdot 3 x^{2} y x^{2}$ .

Assumptions
1. We are given two expressions to multiply: $6xy^{3}z$ and $3x^{2}yx^{2}$ .
2. We need to apply the laws of exponents and multiplication to simplify the expression.

First, we will multiply the coefficients (numerical parts) of the two expressions.
$6 \times 3$

Calculate the product of the coefficients.
$6 \times 3 = 18$

Next, we will multiply the variables with the same base by adding their exponents according to the laws of exponents.
For the variable $x$ , we have $x^1$ from the first expression and $x^{2+2}$ from the second expression.

Add the exponents of $x$ .
$1 + (2 + 2) = 5$

For the variable $y$ , we have $y^3$ from the first expression and $y^1$ from the second expression.

Add the exponents of $y$ .
$3 + 1 = 4$

For the variable $z$ , we only have $z^1$ from the first expression and no $z$ in the second expression.

Since there is only one $z$ , its exponent remains as $1$ .

Combine the results from steps 3, 5, 7, and 9 to write the simplified expression.
$18x^5y^4z$
The simplified result of multiplying and simplifying $6xy^{3}z \cdot 3x^{2}yx^{2}$ is $18x^5y^4z$ .