Assuming that x, y, z are positive real numbers, simplify each of the following:

(i) (ii) (iii) (x^-2/3y^-1/2)² (iv) (v) (vi)

Simplify:

(i) (16^-1/5)^5/2 (ii) (iii) (0.001)^1/3 (iv) (v) (vi)

Prove that:

(i)

(ii) 9^3/2 -3× 5⁰ - = 15

(iii) -3×8^2/3 ×4⁰+

(iv) = 10

(v) + (0.01)^-1/2 – (27)^2/3 =

(vi)

(vii)

(viii) = 28

(ix)

If 27^x =, find x.

Find the values of x in each of the following:

(i) 2^5x÷ 2^x =

(ii) (2³)⁴ = (2²)^x

(iii)

(iv) 5^x-2 × 3^2x-3 = 135

(v) 2^x-5 × 5^x-4 = 5

(vi) 2^x-7 × 5^x-4 = 1250

Write (625)^-1/4 in decimal form.

State the product law of exponents.

State the quotient law of exponents.

State the power law of exponents.

For any positive real number x, find the value of

Write the value of {5(8^1/3 + 27^1/3)³}^1/4

Simplify [{(625)^-1/2}^-1/4]².

For any positive real number x, write the value of

If (x-1)³ = 8, what is the value of (x+1)²

If 2⁴×4² = 16x, then find the value of x.

If 3^x-1=9 and 4^y+2 = 64, What is the value of .

Write the value of .

Write × (64)^-1/3 as a rational number.

Write the value of.

The value of {2-3(2-3)³}³ is

(256)^0.16 × (256)^0.09

If 10^2y = 25, then 10^-y equals

The value of x-y^x-y when x = 2 and y = -2 is

The product of the square root of x with the cube root of x is

If 9^x+2 = 240 + 9^x, then x =

The seventh root of x divided by the eighth root of x is

The square root of 64 divided by the cube root of 64 is

Which of the following is (are) not equal to ?

When simplified (x^-1 + y^-1)^-1 is equal to

If 8^x+1 = 64, what is the value of 3^2x+1?

If 0 < y < x, which statement must be true?

If x is a positive real number and x² = 2, then x³ =

If (2³)² = 4^x, then 3^x =

If 10^x = 64, what is the value of?

If = 8x^-1 and x > 0, then x =

If g = t^2/3 + 4t^-1/2, what is the value of g when t = 64?

If x^-2 = 64, then x^1/3 + x⁰ =

If 4^x – 4^x-1 = 24, then (2x)^x equals

When simplified is

Which one of the following is not equal to ?

Which one of the following is not equal to ?

When simplified is

is equal to

If a, b, c are positive real numbers, then is equal to

If, then x =

If , then x=

The value of is

If a, b, c are positive real numbers, then is equal to

The value of 64^-1/3 (64^1/3 – 64^2/3), is

If = 125, then 5 =

If (16)^2x+3 =(64)^x+3, then 4^2x-2 =

If a, m, n are positive integers, then is equal to

If 2^-m×, then is equal to

If x = 2 and y = 4, then +=

The value of m for which = 7^m, is

The value of {(23+2²)^2/3+(140 – 19)^1/2}², is

If = 1024, then=

If = 3⁷, then x =