HOW TO SIMPLIFY EXPONENTIAL EXPRESSIONS

To simplify exponential expressions, we can use the required rules from exponents.

  1. xm⋅ xn  =  xm+n
  2. (xy)m  =  xm ⋅ ym
  3. xm ÷ xn  =  xm-n
  4. (x/y)m  =  xm/ym
  5. (xm)n  =  xmn
  6. x-m  =  1/xm

Problem 1 :

x4/x

Solution :

Step 1 :

x4/x1

Step 2 :

= x4 · x-1

Step 3 :

Since the bases are the same, use one base and combine the powers.

= (x4 – 1)

= x3

Problem 2 :

4b2 × 2b3

Solution :

Step 1 :

4b2 × 2b3

Step 2 :

Since the bases are the same, use one base and combine the powers and multiply the coefficients.

= 8(b2 + 3)

 = 8b5

Problem 3 :

a6b3/ a4b

Solution :

Step 1 :

a6b3/a4b1

Step 2 :

= a6b3 · a-4b-1

Step 3 :

Since the bases are same, combine the powers.

= (a6 – 4 · b3 – 1)

= a2 · b2

Problem 4 :

18x6/3x3

Solution :

Step 1 :

18x6/3x3

Step 2 :

Dividing the coefficients.

6x6/x3

Step 3 :

= 6(x6 · x-3)

Since the bases are same, use one base and combine the powers.

= 6(x6 – 3)

= 6x3

Problem 5 :

5x3y2/15xy

Solution :

Step 1 :

5x3y2/15xy

Step 2 :

Dividing the coefficients.

= x3y2/3xy

Step 3 :

= 1/3 (x3y2 · x-1y-1)

Since the bases are same, use one base and combine the powers.

= 1/3(x3 – 1  · y2 – 1)

= 1/3 (x2 · y)

Problem 6 :

24t6 r4/15t6r2

Solution :

24t6 r4/15t6r2

Dividing the coefficients.

= 8t6 r4/5t6r2

= 8/5(t6 r4 /t6r2)

= 8/5(t6 6 · r4 – 2)

= 8/5(t0 · r2)

= 8r2/5

Problem 7 :

3pq3 × 5p5

Solution :

= 3pq3 × 5p5

= 15(p1 + 5  · q3)

= 15p6q3

Problem 8 :

x12/(x3)2

Solution :

x12/(x3)2

= x12/x6

= x12 · x-6

= x(12 – 6)

= x6

Problem 9 :

(t6 × t4)/(t2)3

Solution :

(t6 × t4)/(t2)3

= (t6 × t4)/(t6)

= t4  

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