HOW TO SIMPLIFY EXPONENTIAL EXPRESSIONS

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.

= (x^{4 – 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(b^{2 + 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.

= (a^{6 – 4} · b^{3 – 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(x^{6 – 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(x^{3 – 1}  · y^{2 – 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(t^{6 – 6} · r^{4 – 2})

= 8/5(t⁰ · r²)

= 8r²/5

Problem 7 :

3pq³ × 5p⁵

Solution :

= 3pq³ × 5p⁵

= 15(p^{1 + 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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