Question Simplify expressions like $a^3$ , $6yx$ , $4x^2$ , $15x^2y$ , and $-4y^2z^2$ .

Studdy Solution

STEP 1

1. The expressions involve multiplication of variables and constants, which is commutative and associative.
2. The expressions can be simplified by combining like terms and using the properties of exponents for variables.
3. The final expressions should be in simplified form, with constants multiplied together and variables with the same base combined using exponents.

STEP 2

1. Simplify each expression by combining like terms and constants.
2. Apply the properties of exponents for variables with the same base.

STEP 3

Simplify expression (a) $a \times a \times a$ by combining like terms.
$a \times a \times a = a^3$

STEP 4

Simplify expression (b) $2 \times y \times 3 \times x$ by first multiplying the constants together and then writing the variables next to each other.
$2 \times y \times 3 \times x = 6xy$

STEP 5

Simplify expression (c) $4 \times x \times x$ by recognizing that $x \times x$ is $x^2$ and then multiplying by the constant.
$4 \times x \times x = 4x^2$

STEP 6

Simplify expression (d) $3 \times y \times 5 \times x \times x$ by first multiplying the constants together and then using the properties of exponents for the variable $x$ .
$3 \times y \times 5 \times x \times x = 15yx^2$

STEP 7

Simplify expression (e) $-4 \times z \times y \times z \times y$ by first multiplying the constant with the negative sign and then combining the like variables using the properties of exponents.
$-4 \times z \times y \times z \times y = -4y^2z^2$
The simplified expressions are as follows: a) $a^3$ b) $6xy$ c) $4x^2$ d) $15yx^2$ e) $-4y^2z^2$

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Question Simplify expressions like $a^3$ , $6yx$ , $4x^2$ , $15x^2y$ , and $-4y^2z^2$ .

Studdy Solution

STEP 1

STEP 2

1. Simplify each expression by combining like terms and constants.
2. Apply the properties of exponents for variables with the same base.

STEP 3

Simplify expression (a) $a \times a \times a$ by combining like terms.
$a \times a \times a = a^3$

STEP 4

Simplify expression (b) $2 \times y \times 3 \times x$ by first multiplying the constants together and then writing the variables next to each other.
$2 \times y \times 3 \times x = 6xy$

STEP 5

Simplify expression (c) $4 \times x \times x$ by recognizing that $x \times x$ is $x^2$ and then multiplying by the constant.
$4 \times x \times x = 4x^2$

STEP 6

Simplify expression (d) $3 \times y \times 5 \times x \times x$ by first multiplying the constants together and then using the properties of exponents for the variable $x$ .
$3 \times y \times 5 \times x \times x = 15yx^2$

STEP 7

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Question Simplify expressions like a3a^3a3, 6yx6yx6yx, 4x24x^24x2, 15x2y15x^2y15x2y, and −4y2z2-4y^2z^2−4y2z2.

Studdy Solution

STEP 1

STEP 2

1. Simplify each expression by combining like terms and constants.2. Apply the properties of exponents for variables with the same base.

STEP 3

Simplify expression (a) a×a×aa \times a \times aa×a×a by combining like terms.a×a×a=a3 a \times a \times a = a^3 a×a×a=a3

STEP 4

Simplify expression (b) 2×y×3×x2 \times y \times 3 \times x2×y×3×x by first multiplying the constants together and then writing the variables next to each other.2×y×3×x=6xy 2 \times y \times 3 \times x = 6xy 2×y×3×x=6xy

STEP 5

Simplify expression (c) 4×x×x4 \times x \times x4×x×x by recognizing that x×xx \times xx×x is x2x^2x2 and then multiplying by the constant.4×x×x=4x2 4 \times x \times x = 4x^2 4×x×x=4x2

STEP 6

Simplify expression (d) 3×y×5×x×x3 \times y \times 5 \times x \times x3×y×5×x×x by first multiplying the constants together and then using the properties of exponents for the variable xxx.3×y×5×x×x=15yx2 3 \times y \times 5 \times x \times x = 15yx^2 3×y×5×x×x=15yx2

STEP 7

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Question Simplify expressions like $a^3$ , $6yx$ , $4x^2$ , $15x^2y$ , and $-4y^2z^2$ .

1. Simplify each expression by combining like terms and constants.
2. Apply the properties of exponents for variables with the same base.

Simplify expression (a) $a \times a \times a$ by combining like terms.
$a \times a \times a = a^3$

Simplify expression (b) $2 \times y \times 3 \times x$ by first multiplying the constants together and then writing the variables next to each other.
$2 \times y \times 3 \times x = 6xy$

Simplify expression (c) $4 \times x \times x$ by recognizing that $x \times x$ is $x^2$ and then multiplying by the constant.
$4 \times x \times x = 4x^2$

Simplify expression (d) $3 \times y \times 5 \times x \times x$ by first multiplying the constants together and then using the properties of exponents for the variable $x$ .
$3 \times y \times 5 \times x \times x = 15yx^2$