Solve: (17^-3 × 17^3x)/17 - 17x Using Exponent Rules

Question

17−3⋅173x17−17x=? \frac{17^{-3}\cdot17^{3x}}{17}-17x=\text{?}

Video Solution

Solution Steps

00:00 Simply
00:09 In order to eliminate a negative exponent
00:12 We'll flip numerator and denominator and the exponent will become positive
00:15 We'll use this formula in our exercise, and convert from fraction to exponent
00:20 When multiplying powers with equal bases
00:23 The exponent of the result equals the sum of the exponents
00:28 We'll use this formula in our exercise, we'll sum the exponents
00:41 And this is the solution to the question

Step-by-Step Solution

Let's deal with the first term in the problem, which is the fraction,

For this, we'll recall two laws of exponents:

a. The law of exponents for multiplication between terms with identical bases:

am⋅an=am+n a^m\cdot a^n=a^{m+n} b. The law of exponents for division between terms with identical bases:

aman=am−n \frac{a^m}{a^n}=a^{m-n} Let's apply these laws of exponents to the problem:

17−3⋅173x17−17x=17−3+3x17−17x=17−3+3x−1−17x=173x−4−17x \frac{17^{-3}\cdot17^{3x}}{17}-17x=\frac{17^{-3+3x}}{17}-17x=17^{-3+3x-1}-17x=17^{3x-4}-17x where in the first stage we'll apply the law of exponents mentioned in 'a' above to the fraction's numerator, and in the next stage we'll apply the law of exponents mentioned in 'b' to the resulting expression, then we'll simplify the expression.

Therefore, the correct answer is answer a.

Answer

173x−4−17x 17^{3x-4}-17x

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Related Subjects

Negative Exponents Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Division of Exponents with the Same Base Multiplying Exponents with the Same Base Exponents - Special Cases

Question Types

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