F3 mathematics chp1

Simplify each of the following.

9²x9²

Choose the correct answer.

$$2^{p+p+p+p+p+p+p}$$

$$27^{\frac{1}{3}}=\sqrt[3]{27}$$

$$\frac{\left(3x^2y^4\right)^{\frac{1}{2}}\times3^{\frac{3}{2}}x^2y^3}{18x^2y^{-3}}$$

Given $$9\left(3^{2x-1}\right)\div81^x=27,$$ calculate the value of x.

Given $$4\left(16^x\right)=64^{2-x}\div256$$ , calculate the value of x.

Write 4096 in index form using

(i)base of 8

(ii)index of 12

Solve the following simultaneous equations.

$$64^x\times2^{2y}=2^2\ and\ 3^x\times\frac{1}{3^y}=27$$

$$9^{2x^2}\times9^x=9^6$$

Find the possible values of x for the following equation.

$$\frac{\left(81h^6\right)^{\frac{1}{2}}}{3k^3}\times h^3k^9$$

Simplify.