Question

16. Simplify:
(i) [{2p-q²r}³]‐²​

Answer 1

(((3p2qr(-2))/(2p(-1)q3))2)/(2p3r)(-1)

Final result :

9p9

—————

2q4r3

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-1" was replaced by "^(-1)". 2 more similar replacement(s)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(((3•(p2))•q)•(r-2))

{————————————————————}2

((2•(p-1))•(q3)) ((

Step 2 :

Equation at the end of step 2 :

(((3•(p2))•q)•(r-2))

{————————————————————}2

(2p(-1)•(q3)) (2

Step 3 :

Equation at the end of step 3 :

((3p2 • q) • r(-2))

{———————————————————}2 ÷ (2)(-1)p(-3)r(-1)

(2p(-1)q3)

Step 4 :

3p2qr(-2)

Simplify —————————

2p(-1)q3

Dividing exponential expressions :

4.1 p2 divided by p(-1) = p(2 - (-1)) = p3

Dividing exponential expressions :

4.2 q1 divided by q3 = q(1 - 3) = q(-2) = 1/q2

Equation at the end of step 4 :

((3p3)

(———————)2) ÷ (2)(-1)p(-3)r(-1)

(2q2r2)

Step 5 :

5.1 p3 raised to the 2 nd power = p( 3 * 2 ) = p6

5.2 q2 raised to the 2 nd power = q( 2 * 2 ) = q4

5.3 r2 raised to the 2 nd power = r( 2 * 2 ) = r4

Equation at the end of step 5 :

32p6

—————— ÷ (2)(-1)p(-3)r(-1)

22q4r4

Step 6 :

32p6

Divide —————— by (2)(-1)p(-3)r(-1)

22q4r4

Multiplying exponential expressions :

6.1 r4 multiplied by r(-1) = r(4 + (-1)) = r3

Dividing exponential expressions :

6.2 p6 divided by p(-3) = p(6 - (-3)) = p9

Dividing exponents :

6.3 21 divided by 22 = 2(1 - 2) = 2(-1) = 1/21 = 1/2

Final result :

9p9

—————

2q4r3