SIMPLIFY THE FOLLOWING EXPONENTIAL EXPRESSION

Decide whether the expression has been simplified correctly.

Problem 1 :

 (ab)⁸ = ab⁸

A) Yes          B) No

Solution :

Option B) is correct.

Product rule :

(ab)^m = a^m ⋅ b^m

(ab)⁸ = a⁸ ⋅ b⁸

But the given expression is (ab)⁸ = ab⁸ not correct.

The expression has been not simplified correctly.

Problem 2 :

(a/4)⁵ = a⁵/4

A) Yes          B) No

Solution :

Option B) is correct.

(a/4)⁵ = a⁵/4

(a/4)⁵ = a⁵/4⁵

But the given expression is (a/4)⁵ = a⁵/4 not correct.

The expression has been not simplified correctly.

Apply the product rule for exponents, if possible.

Problem 3 :

(-3x⁵y)(-4x⁹y²)

A) 12x⁴⁵y²      B) -12x¹⁴y²      C) 12x¹⁵y³       D)12x¹⁴y³

Solution :

= (-3x⁵y)(-4x⁹y²)

= (-3) ⋅ (-4) ⋅ x⁵ ⋅ x⁹ ⋅ y ⋅ y²

= 12x¹⁴y³

Option D) is correct.

Evaluate the expression.

Problem 4 :

10⁰ + 5⁰

A) 0      B) 1       C) 15      D)2

Solution :

= 10⁰ + 5⁰

= 1 + 1

= 2

Option D) is correct.

Problem 5 :

-10⁰

A) -10      B) 1       C) -1        D)0

Solution :

-10⁰

Any thing to the power of zero is 1.

= -1

Option C) is correct.

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.

Problem 6 :

5x^-2

A) 1/5x²        B) -10x         C) 5/x²        D)1/25x²

Solution :

5x^-2

= 5 × 1/x²

= 5/x²

Option C) is correct.

Problem 7 :

(-a)^-18

A) 1/a¹⁸         B) 18a          C) 1/-a¹⁸       D)1/a^-18

Solution :

(-a)^-18

= a^-18

a^-n = 1/aⁿ

= 1/a¹⁸

Option A) is correct.

Evaluate the expression.

Problem 8 :

5^-4/6^-3

A) 1296/3125     B) 216/625      C) 3125/1296    D)625/216

Solution :

5^-4/6^-3

a^-n = 1/aⁿ

= 6³/5³

= 216/625

Option B) is correct.

Problem 9 :

1/-3^-3

A) -9      B) -27        C) 9        D)27

Solution :

1/-3^-3

= -1/3^-3

By flipping the base, we can covert the negative exponent as positive exponent.

= -3³

= -27

Option B) is correct.

Problem 10 :

(2/7)^-3

A) -343/8      B) 8/343      C) -8/343     D)343/8

Solution :

(2/7)^-3

Since we have negative exponents, by taking the reciprocal we can convert it as reciprocal.

= (7/2)³

= 343/8

Option D) is correct.