Sure! Let's simplify each of these expressions step-by-step.
### a) [tex]\(x \times x \times x \times y \times y\)[/tex]
1. Identify Repeated Factors:
- We have three factors of [tex]\(x\)[/tex]: [tex]\(x \times x \times x\)[/tex]
- We have two factors of [tex]\(y\)[/tex]: [tex]\(y \times y\)[/tex]
2. Apply the Rules of Exponents:
- The rule of exponents states that when you multiply the same base with exponents, you add the exponents:
[tex]\[
x \times x \times x = x^3
\][/tex]
[tex]\[
y \times y = y^2
\][/tex]
3. Combine the Results:
- Put together the simplified parts:
[tex]\[
x^3 \times y^2
\][/tex]
Therefore, the simplified form of [tex]\(x \times x \times x \times y \times y\)[/tex] is:
[tex]\[x^3 \times y^2\][/tex]
### b) [tex]\(2 \times x \times x \times 3 \times y \times y \times y\)[/tex]
1. Identify Repeated Factors:
- We have two factors of [tex]\(x\)[/tex]: [tex]\(x \times x\)[/tex]
- We have three factors of [tex]\(y\)[/tex]: [tex]\(y \times y \times y\)[/tex]
2. Simplify Numeric Multiplication:
- First, simplify the constants (2 and 3):
[tex]\[
2 \times 3 = 6
\][/tex]
3. Apply the Rules of Exponents:
- The rule of exponents states that when you multiply the same base with exponents, you add the exponents:
[tex]\[
x \times x = x^2
\][/tex]
[tex]\[
y \times y \times y = y^3
\][/tex]
4. Combine the Results:
- Combine the numeric and variable parts:
[tex]\[
6 \times x^2 \times y^3
\][/tex]
Therefore, the simplified form of [tex]\(2 \times x \times x \times 3 \times y \times y \times y\)[/tex] is:
[tex]\[6 \times x^2 \times y^3\][/tex]
In summary:
a) The simplified form of [tex]\(x \times x \times x \times y \times y\)[/tex] is [tex]\(x^3 \times y^2\)[/tex].
b) The simplified form of [tex]\(2 \times x \times x \times 3 \times y \times y \times y\)[/tex] is [tex]\(6 \times x^2 \times y^3\)[/tex].
