Rules of Multiplication of Terms

Q.

Multiply the binomials: $(2x+5)$ and $(4x-3)$

Q. The value of $a^m\times a^n$ is equal to $a^{mn}$.

1. True
2. False

Q.

Choose the correct option and fill in the blanks :

${\left(1^{100}\right)}^2=\_\_\_\_\_\_\_\_.$

Q.

$Y$ red balloons and $m$ green balloons were divided evenly among three kids. How many balloons did each kid get?

Q.

Using laws of exponents, simplify and write the answer in exponential form:

$7^x\times 7^2$

Q. Find the value of $7ab\times 4ab\times 2ab$.

1. $28a^2{b}^2$
2. $56a^2{b}^2$
3. $28a^3{b}^3$
4. $56a^3{b}^3$

Q.

Identify the numerical coefficient, exponent, and variable for the following term: $7x^3$

Q. Multiply $uv$ with $5u+2v$.

1. $5u{v}^2+2u^{2}v$
2. $5u^{2}v+2u{v}^2$
   

Q. In a company, soldiers are arranged in rows and columns, with $x$ representing the number of soldiers in each row and $y$ representing the number of soldiers in each column. Calculate the company's total number of soldiers.

1. $\frac{x}{y}$
2. $xy$
3. $x+y$

Q. The value of the product $6xy\times 12x^2{y}^2$ is same as the value of product?

1. $72x^2{y}^2$
2. $12xy\times 6xy$
3. $12x^2{y}^2\times 6xy$
4. $12x^2{y}^2\times 6x^2{y}^2$

Q.

What is the simplified form of the expression?

$x^8·2y^{10}·5x^5$

Q. A rectangle has width of $w$ inches and height of $h$ inches . Area(in inch${}^2$) of the rectangle is

1. $(h+w)$
2. $(h\times w)$
3. $\frac{h}{w}$

Q. If $a$ is the length of a rectangle and $b$ is the breadth of the rectangle, then find $(Area{)}^m+(Perimeter{)}^n$ in terms of $a$ and $b$.

1. $(a\times b{)}^n+(a+b{)}^n$
2. $(a\times b{)}^m+(a+b{)}^m$
3. $(a\times b{)}^m+2^n(a+b{)}^n$
4. $(a+b{)}^m+(a+b{)}^n$

Q. $2a^{2}b\times 6a{b}^2=$

1. $12a^3{b}^3$
2. $12a^2{b}^2$
3. $8a^2{b}^2$

Q.

MULTIPLYING AND DIVIDING IN SCIENTIFIC NOTATION

Find the product or quotient. Write your answer in scientific notation.

$(5.8\times {10}^{-6})÷(2\times {10}^{-3})$

Q. The area of the rectangle in the diagram shown below is .

1. $np+mp+nq+mq$
2. $pq+mn+mn+qp$
3. $(n+p)\times (m+q)$

Q. Simplify $9z^2\times 10z^3$.

1. $90z^5$
2. $90z^6$
3. $19z^5$

Q. Simplify:
$2x^4\times \frac{1}{2}{x}^6$

1. $x^{24}$
2. $x^{10}$
3. $2x^{10}$

Q. Simplify:
$9w^3\times 3w^9$

1. $27w^{27}$
2. $27w^{12}$
3. $12w^{12}$

Q. $(-x)\times (-y-z)=$

1. $-xy+xz$
2. $xy-xz$
3. $xy+xz$

Q. Multiplying $-7a^2$ with $-8a^5$ gives:

1. $56\times a^7$
2. $-56\times a^7$
3. $-15\times a^7$
4. $56\times a^{10}$

Q. $y\times y^3=$

1. $y^4$
2. $4y$
3. Cannot be simplified

Q. $2x\times \frac{3}{x}=$

Q. $3y\times 2y^3$ equals

1. $6y^3$
2. $5y^4$
3. $6y^4$

Q. $24u^2{v}^{3}w\times 8vw=$

1. $192u^2{v}^4{w}^2$
2. $192u^0{v}^4{w}^2$
3. $32u^2{v}^4{w}^2$

Q. $(x{y}^2+2z)\times 2xy=$

1. $=2x^2{y}^3+4xyz$
2. $2x^3{y}^2+4xyz$
3. $=2x^2{y}^3+2xyz$

Q. In the figure given below, what does $a\times b$ and $2(a+b)$ respectively represent?

1. Area of rectangle and perimeter of rectangle
2. Perimeter of rectangle and area of rectangle
3. Length of rectangle and breadth of rectangle
4. Breadth of rectangle and length of rectangle