Operations on Exponents in Algebraic Expansions

Q.

Multiply the binomials: $\left(2pq+3q^2\right)$ and $\left(3pq-2q^2\right)$

Q.

$7^9+9^7$ is divided by

1. $128$

2. $24$

3. $64$

4. $72$

Q.

How do you evaluate and simplify ${27}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$?

Q.

Simplify $9^{\frac{3}{2}}$.

Q.

Show that: ${(4\mathrm{pq}+3\mathrm{q})}^2-{(4\mathrm{pq}-3\mathrm{q})}^2=48{\mathrm{pq}}^2$

Q. If $\frac{a^{2b-3}\times {\left(a^2\right)}^{b+1}}{{\left(a^4\right)}^{-3}}=(a^3{)}^3÷(a^6{)}^{-3}$, then find the value of $2b$.

1. 8
2. 24
3. 4
4. 16

Q.

Multiply the following:

$25x{y}^2,8x^3+2x{y}^2+9x^{2}y+27y^3$

Q.

Verify that $x^3+y^3+z^3-3xyz=$ $\frac{1}{2}\left(x+y+z\right)[{(x-y)}^2+{(y-z)}^2+{(z-x)}^2]$

Q. Yolanda sent a photo of her and her family on vacation to nine Facebook friends. If each of them sends it to five of their friends, and each of those friends sends it to five of their friends, and those friends send it to five more, how many people (not counting Yolanda herself) will see her photo? No friend received the photo twice. Express your answer in exponential notation.

1. $9+5+5^2+5^3$
2. $9(1+5+5^2+5^3)$
3. $1+5+5^2+5^3$
4. None of the above

Q. Expand the algebraic expression $x^3(2x^4+4x^3+5).$

1. $2x^7+4x^6+5x^3$
2. $2x^7+4x^6+15x^3$
3. $2x^{12}+4x^9+5x^3$
4. $2x^{12}+4x^9+15x^3$

Q.

Evaluate the value of the following:

$\frac{9^2\times 8^2}{72}$

Q. Expand the algebraic expression $a^{\frac{1}{2}}(a^{\frac{1}{2}}+a^{\frac{-1}{2}})$

1. $a$
2. $a+1$
3. $a+2$
4. $a+3$

Q. Use the properties of exponents to write an equivalent expression that is a product of distinct primes, each raised to an integer power for the expression (${10}^6$$\times$ $9^2$)/$6^4$

1. $2^3$\times5^6$
2. $2^3$\times5^5$
3. $2^2$\times5^6$
4. $2^2$\times5^5$

Q.

The reciprocal of $x^{-1}$ is $\frac{1}{x}$ State whether the statement is true (T) or false (F).

1. True
2. False

Q. Expand the algebraic expression $(3a^2+2b^3)(3a^2-2b^3).$

1. $9a^4-4b^9$
2. $9a^4-4b^6$
3. $3a^4-2b^6$
4. $3a^4-2b^9$

Q. Expand the algebraic expression $5^x(5^x+2)$

1. $5^x+2\left(5^x\right)$
2. $5^{2x}+2\left(5^x\right)$
3. $5^{3x}+2\left(5^x\right)$
4. $5^{-2x}+2\left(5^x\right)$

Q.

Evaluate $\frac{{\left(2^2\right)}^3}{2^5}$

Q. Expand the algebraic expression $x^2(x^3-3x^2-4)$

1. $x^5-3x^4-4x^2$
2. $x^5+3x^4-4x^2$
3. $x^5-3x^4+4x^2$
4. $x^5-3x^3-4x^2$

Q. Expand the algebraic expression $a^{\frac{1}{3}}(a^{\frac{3}{2}}+a^3)$

1. $a^{\frac{11}{6}}+a^{\frac{10}{3}}$
2. $a^{\frac{11}{6}}+a^{\frac{7}{3}}$
3. $a^{\frac{7}{6}}+a^{\frac{10}{3}}$
4. $a^{\frac{5}{6}}+a^{\frac{10}{3}}$

Q. What is the area of a rectangular park with length $(a^2+2ab+b^2)$ units and width $(a+b)$ units $?$

1. $a^3+3a^{2}b+3a{b}^2+b^3$
2. $a^3+3a^{3}b+3a{b}^3+b^3$
3. $a^3+4a^{2}b+a{b}^2+b^3$
4. None of the above

Q. Expand the algebraic expression $x^2(x^3-3x^2-4)$

1. $x^5-3x^4-4x^2$
2. $x^5+3x^4-4x^2$
3. $x^5-3x^4+4x^2$
4. $x^5-3x^3-4x^2$

Q.

Multiply the following :

$\left(2x\right)\times \left(4x^2+\frac{7}{3}{y}^{2}z-2xy\right)$

Q. Expand the algebraic expression $a^{\frac{1}{3}}(a^{\frac{3}{2}}+a^3)$

1. $a^{\frac{11}{6}}+a^{\frac{10}{3}}$
2. $a^{\frac{11}{6}}+a^{\frac{7}{3}}$
3. $a^{\frac{7}{6}}+a^{\frac{10}{3}}$
4. $a^{\frac{5}{6}}+a^{\frac{10}{3}}$

Q.

Evaluate the value of the following:

${\left(\frac{6}{11}\right)}^2÷{\left(\frac{6}{11}\right)}^2$

Q. Expand the algebraic expression $5^x(5^x+2)$

1. $5^x+2\left(5^x\right)$
2. $5^{2x}+2\left(5^x\right)$
3. $5^{3x}+2\left(5^x\right)$
4. $5^{2x}+2\left(5^x\right)$

Q. Natasha says that $7^5$ is bigger than $5^7$. Has Natasha arrived at the right answer?

1. Yes
2. No
3. Cannot be determined

Q.

Find the following products:

$\left(2x^2+y^3\right)\left(2x^2+y^3\right)$

Q.

Fill in the blanks :

$\frac{3^7}{3^4\times 3^3}=\_\_\_\_\_\_\_\_$

Q. Which of the following option is equal to $3x^2{y}^3(4x^3+2x{y}^2+x^{-2}{y}^{-3})$ for $x,y\ne 0?$

1. $12x^5{y}^3+6x^5{y}^3+3$
2. $12x^5{y}^3+6x^3{y}^5$
3. $12x^5{y}^3+6x^3{y}^5+3$
   
4. $12x^3{y}^5+6x^3{y}^5+3$

Q.

Evaluate the value of the following:

$\frac{3^5\times 5^5}{{\left(15\right)}^3}$