Indices F3

 $Given\ \ -343\ =\ \left(-7\right)^y.$  

Find the value of y

• 3

• 2

• 5

• 4

 $3^2\ \times\ 3^5\ \div3^y\ =3^3$  
Find the value of y

• 2

• 4

• 6

• 7

 $5^x\ \times\ 125^{x-y}\ =\ 25$  

Express x in term of y

•  $x\ =\frac{3\ +2y}{3}$  

•  $x\ =\ \frac{5\ +\ 2y}{4}$  

•  $x=\frac{2+3y}{4}$  

•  $x\ =\ \frac{4\ +3y}{3}$  

Calculate the value of the following :

 $\frac{\left(-5x\right)^2\ \times\ \left(2x^{5\ }y^{-3}\right)^3}{120\ x^3y^2}$  

•  $\frac{4x^{15}}{3y^{11}}$  

•  $\frac{3x^{11}}{5y^{14}}$  

•  $\frac{4x^{12}}{5y^{11}}$  

•  $\frac{5x^{14}}{3y^{11}}$  

Which of the following is not equal to

 $x^3\ y^5$  

•  $x^3\ \times y^2\ \div y^7$  

•  $\left(xy\right)^3\ \times\ y^2$  

•  $\left(xy\right)^7\ \div\ x^4\ y^2$  

•  $\left(x^{-3}\right)\ \times x^{6\ }y^5$  

Find the value of n for

 $64^n\ =\ 8^{3-n}$  

• 2

• 1

• 3

• 4

Calculate the possible values of x for the equation

 $3^{x^2}\ \times\ 3^{5x}\ =3^{24}$  

• x = 2 and x = -8

• x = -3 and x = 8

• x = 3 and x= -8

• x = 8 and x = -3

Simplify :

 $\frac{9^{16}}{9^3\ \times\left(9^5\right)^2}$  

•  $9^{29}$  

•  $9^{26}$  

•  $9^5$  

•  $9^3$  

 $5p^2\ \times4p^6\ \times p\ =$  

•  $20p^9$  

•  $9p^9$  

•  $20p^{11}$  

•  $20p^{12}$  

Find the value of :

 $36^{-\frac{1}{2}}\ \times8^{\frac{2}{3}}$  

•  $\frac{1}{2}$  

•  $\frac{2}{3}$  

•  $\frac{3}{2}$  

•  $\frac{9}{2}$