Multiply:

1. [tex]a \times a \times a = [/tex]
2. [tex]3a \times 3a \times 3a = [/tex]
3. [tex]a^2 \times a^3 = [/tex]
4. [tex]4a^2 \cdot 5a^b = [/tex]

(b) [tex](-5x^2)(3x) = [/tex]

(v) [tex](6b^5)(-2ab^4) = [/tex]

(8) [tex]11m^3n \times (-2m^3) = [/tex]



Answer :

Sure, I'll solve each of the given questions step-by-step.

1. [tex]\(a \times a \times a\)[/tex]

When multiplying the same base number, you add the exponents. Here, we have [tex]\(a\)[/tex] multiplied by itself three times:

[tex]\[ a \times a \times a = a^3 \][/tex]

2. [tex]\(3a \times 3a \times 3a\)[/tex]

Again, when multiplying numbers and variables, you multiply the coefficients (numbers) together and then add the exponents of the variables:

[tex]\[ (3a) \times (3a) \times (3a) = 3 \times 3 \times 3 \times a \times a \times a = 27a^3 \][/tex]

3. [tex]\(a^2 \times a^3\)[/tex]

When multiplying terms with the same base, you add the exponents:

[tex]\[ a^2 \times a^3 = a^{2+3} = a^5 \][/tex]

4. [tex]\(4a^2 \cdot 5a^b\)[/tex]

First, multiply the coefficients (4 and 5), then add the exponents of the common bases (since both terms have [tex]\(a\)[/tex]):

[tex]\[ 4a^2 \cdot 5a^b = 4 \times 5 \times a^{2+b} = 20a^{2+b} \][/tex]

b. [tex]\(\left(-5x^2\right)(3x)\)[/tex]

Multiply the coefficients (-5 and 3) and add the exponents of [tex]\(x\)[/tex]:

[tex]\[ (-5x^2)(3x) = -5 \times 3 \times x^{2+1} = -15x^3 \][/tex]

v. [tex]\(\left(6b^5\right)\left(-2ab^4\right)\)[/tex]

Again, multiply the coefficients (6 and -2), and add the exponents of the common bases (here, [tex]\(b\)[/tex]):

[tex]\[ (6b^5)(-2ab^4) = 6 \times -2 \times a \times b^{5+4} = -12ab^9 \][/tex]

8. [tex]\(11m^3n \times (-2m^3)\)[/tex]

Multiply the coefficients (11 and -2), and add the exponents of the common bases (here, [tex]\(m\)[/tex]):

[tex]\[ 11m^3n \times (-2m^3) = 11 \times -2 \times m^{3+3} \times n = -22m^6n \][/tex]

So, the final answers are:

1. [tex]\(a^3\)[/tex]
2. [tex]\(27a^3\)[/tex]
3. [tex]\(a^5\)[/tex]
4. [tex]\(20a^{2+b}\)[/tex]
b. [tex]\(-15x^3\)[/tex]
v. [tex]\(-12ab^9\)[/tex]
8. [tex]\(-22m^6n\)[/tex]