Solve for n

Solve for n in the equation =1/2

If

Find values of x and y

Rationalize the denominator of the expression

If      , find the values of a, b and c.

Solve equation       

14. Rationalize the denominator to the simplest form:

15. Simplify (-4g⁵)³

 . Find the values of x and y if 

Simplify the expressions:

(i)       

8. If determine the value of

11. Express R as the subject of

6. Express in decimal notation percent of

Solve for x in the equation 9^(x?3) × 81^(1?x) = 27^?x .

11.Rationalize the denominator of the expression 

3.Simplify the expression  

2.Which numbers are equal to their squares? 

  Solve for x in the equation 4^-2x × 8² = 4 × 16^x .

9.Find the value m + n, given that 7^m × 5ⁿ = 875 .

Find the value of x and y if  = 2025

Find the value of x in the equation  

Solve the value of x if 

Express the equation = 1 in terms of P given that P = 3^y. 

(i) Express (?3 + 5)² in the form a + b?3, where a and b are integers.

(ii) Express 

in the form p + q?3, where p and q are rational numbers.

Solve for x if (₈¹₁)^?6x × 81 = ?9 .

Simplify  by rationalizing the denominator.

By using mathematical tables, evaluate  to three significant figures.

Rationalize

Find the value of x for which 2^x ? 16 = ₈¹_x

By rationalizing the denominator, simplify the following expression.

Simplify

(6 marks)

Find the value of x if 8^x-1 = 16

Rationalize the denominator of the expression

Find the value of given that 3^a x 5^b = 675

Without using mathematical tables, evaluate: .

Two quantities are such that

  and , use these quantities to sow that:

(i)

(ii)

Express x in terms of p and q from the formula . Hence, find the value of x if p = 3 and q = -1. 

Find the value of x in the equation 9x3^4x =27^(x-1) 

Rationalize the denominator of 

Use laws of exponents to simplify