Question

algebra i ab
unit 7 exponents
lesson 3 laws of exponents laws 6 & 7 homework
(1-12) simplify each of the following expressions.

1. ( 4ab^0 )
2. ( \frac{1}{x^{-7}} )
3. ( 5x^{-4} )
4. ( \frac{ab^{-4}}{c^{-1}} )

name:

Explanation:

Problem 1: Simplify \( 4ab^0 \)

Step 1: Recall the zero exponent rule

Any non - zero number raised to the power of 0 is 1, i.e., \( a^0 = 1\) for \( a
eq0\). Here, \( b^0 = 1\) (assuming \( b
eq0\)).

Step 2: Substitute \( b^0 = 1\) into the expression

\(4ab^0=4a\times1\)

Step 3: Simplify the expression

\(4a\times1 = 4a\)

Step 1: Recall the negative exponent rule

The negative exponent rule states that \( a^{-n}=\frac{1}{a^n}\), and its reciprocal is \(\frac{1}{a^{-n}}=a^n\) for \( a
eq0\) and \( n\) is an integer.

Step 2: Apply the negative exponent rule

For the expression \(\frac{1}{x^{-7}}\), using the rule \(\frac{1}{a^{-n}} = a^n\) with \( a = x\) and \( n = 7\), we get \(x^{7}\)

Step 1: Recall the negative exponent rule

The negative exponent rule is \( a^{-n}=\frac{1}{a^n}\) for \( a
eq0\) and \( n\) is a positive integer.

Step 2: Apply the negative exponent rule to \(x^{-4}\)

\(x^{-4}=\frac{1}{x^{4}}\)

Step 3: Multiply by the coefficient 5

\(5x^{-4}=5\times\frac{1}{x^{4}}=\frac{5}{x^{4}}\)

Answer:

\(4a\)

Problem 2: Simplify \( \frac{1}{x^{-7}} \)