Question

[{2p^-1q^2r}^3]^-2 simplify

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

Answer 2

Answer:

{(${2p^{-1}q^{2}r}$)³}^{-2}  = $\frac{p^{6}}{64q^{12}r^{6}}$

Step-by-step explanation:

• Simplification: Simplification means to make any equation or expression simple.
• When an expression is in complex form then it is difficult to calculate the required value, so in that case we need to simplify the expression.
• Example: 20% 0f 50 --- it is complex form. Ny simplifying it we can write as $\frac{20}{100}$ × 50 = 10. 10 is the simpler form.

• The given expression:   {(${2p^{-1}q^{2}r}$)³}^{-2}

                                             = (${2p^{-1}q^{2}r}$)^{-6}    [as we know ($a^{x}$)^y = $a^{xy}$]

                                             = $(\frac{{2q^{2}r}}{p})^{-6}$

                                             = $(\frac{p}{2q^{2}r})^{6}$    [∵$x^{-y}$ = $\frac{1}{x^y}$]

                                            = $\frac{p^{6}}{64q^{12}r^{6}}$

                      ∴{(${2p^{-1}q^{2}r}$)³}^{-2}  = $\frac{p^{6}}{64q^{12}r^{6}}$